Would it be the oldest plane in the fleet?
According to this source it is indeed the oldest mainline aircraft in the fleet:
Qantas Fleet Details and History - Planespotters.net
[TABLE="class: DataTable, width: 1242"]
[TR]
[TH="class: dt-first dt-sortable tdReg, align: center"]
Reg[/TH]
[TH="class: nowrap dt-sortable tdCn, align: center"]
c/n[/TH]
[TH="class: nowrap dt-sortable tdLn, align: center"]
ln[/TH]
[TH="class: dt-sortable tdType, align: center"]
Aircraft Type[/TH]
[TH="class: tdConfig, align: center"]Config[/TH]
[TH="class: dt-asc dt-sortable tdDD, align: center"]
Delivered[/TH]
[TH="class: tdPrevReg, align: center"]Prev. Reg[/TH]
[TH="class: tdRemark, align: center"]Remark[/TH]
[TH="class: dt-sortable tdName, align: center"]
Aircraft Name[/TH]
[TH="class: tdAge, align: center"]Age[/TH]
[TH="class: dt-last tdPhotoLink, align: center"][/TH]
[/TR]
[TR="class: dt-odd, bgcolor: #FFFFFF"]
[TD="class: nowrap dt-first, align: center"][/TD]
[TD="align: center"][/TD]
[TD="align: center"][/TD]
[TD="class: nowrap tdType"][/TD]
[TD="class: nowrap, align: center"][/TD]
[TD="class: nowrap dt-asc, bgcolor: #EDF5FF, align: center"][/TD]
[TD="class: nowrap, align: center"][/TD]
[TD="class: remark, align: center"][/TD]
[TD="class: nowrap, align: center"][/TD]
[TD="class: nowrap, align: center"][/TD]
[TD="class: small dt-last, align: center"][/TD]
[/TR]
[TR="class: dt-odd, bgcolor: #FFFFFF"]
[TD="class: nowrap dt-first, align: center"]VH-OJA[/TD]
[TD="align: center"]
24354[/TD]
[TD="align: center"]
731[/TD]
[TD="class: nowrap tdType"]
Boeing 747-438[/TD]
[TD="class: nowrap, align: center"]C56W40Y275[/TD]
[TD="class: nowrap dt-asc, bgcolor: #EDF5FF, align: center"]11-08-1989[/TD]
[TD="class: nowrap, align: center"]
N6046P[/TD]
[TD="class: remark, align: center"][/TD]
[TD="class: nowrap, align: center"]City of Canberra[/TD]
[TD="class: nowrap, align: center"]23.6 Years[/TD]
[TD="class: small dt-last, align: center"]

[/TD]
[/TR]
[TR="class: dt-even"]
[TD="class: nowrap dt-first, align: center"]VH-OJC[/TD]
[TD="align: center"]
24406[/TD]
[TD="align: center"]
751[/TD]
[TD="class: nowrap tdType"]
Boeing 747-438[/TD]
[TD="class: nowrap, align: center"]C56W40Y275[/TD]
[TD="class: nowrap dt-asc, bgcolor: #DBEAFF, align: center"]09-10-1989[/TD]
[TD="class: nowrap, align: center"][/TD]
[TD="class: remark, align: center"][/TD]
[TD="class: nowrap, align: center"]City of Melbourne[/TD]
[TD="class: nowrap, align: center"]23.5 Years[/TD]
[TD="class: small dt-last, align: center"]

[/TD]
[/TR]
[TR="class: dt-odd, bgcolor: #FFFFFF"]
[TD="class: nowrap dt-first, align: center"]VH-OJD[/TD]
[TD="align: center"]
24481[/TD]
[TD="align: center"]
764[/TD]
[TD="class: nowrap tdType"]
Boeing 747-438[/TD]
[TD="class: nowrap, align: center"]C56Y356[/TD]
[TD="class: nowrap dt-asc, bgcolor: #EDF5FF, align: center"]16-01-1990[/TD]
[TD="class: nowrap, align: center"][/TD]
[TD="class: remark, align: center"][/TD]
[TD="class: nowrap, align: center"]Brisbane[/TD]
[TD="class: nowrap, align: center"]23.2 Years[/TD]
[TD="class: small dt-last, align: center"]

[/TD]
[/TR]
[TR="class: dt-even"]
[TD="class: nowrap dt-first, align: center"]VH-OJE[/TD]
[TD="align: center"]
24482[/TD]
[TD="align: center"]
765[/TD]
[TD="class: nowrap tdType"]
Boeing 747-438[/TD]
[TD="class: nowrap, align: center"]C56W40Y275[/TD]
[TD="class: nowrap dt-asc, bgcolor: #DBEAFF, align: center"]26-01-1990[/TD]
[TD="class: nowrap, align: center"][/TD]
[TD="class: remark, align: center"][/TD]
[TD="class: nowrap, align: center"]City of Adelaide[/TD]
[TD="class: nowrap, align: center"]23.1 Years[/TD]
[TD="class: small dt-last, align: center"]

[/TD]
[/TR]
[TR="class: dt-odd, bgcolor: #FFFFFF"]
[TD="class: nowrap dt-first, align: center"]VH-OGG[/TD]
[TD="align: center"]
24929[/TD]
[TD="align: center"]
343[/TD]
[TD="class: nowrap tdType"]
Boeing 767-338(ER)[/TD]
[TD="class: nowrap, align: center"]C30Y224[/TD]
[TD="class: nowrap dt-asc, bgcolor: #EDF5FF, align: center"]12-12-1990[/TD]
[TD="class: nowrap, align: center"][/TD]
[TD="class: remark, align: center"][/TD]
[TD="class: nowrap, align: center"]City of Rockhampton[/TD]
[TD="class: nowrap, align: center"]22.2 Years[/TD]
[TD="class: small dt-last, align: center"]

[/TD]
[/TR]
[/TABLE]
The next youngest batch of aircraft (for mainline) are the oldest remaining 767s, which were delivered in 1990.
Maybe some of the crash 8's would be older.
Not quite, Sunstate's oldest Dash-8 is a 1998 delivery.
Sunstate Airlines (QantasLink) Fleet Details and History
[TABLE="class: DataTable, width: 1242"]
[TR]
[TH="class: dt-first dt-sortable tdReg, align: center"]
Reg[/TH]
[TH="class: nowrap dt-sortable tdCn, align: center"]
c/n[/TH]
[TH="class: dt-sortable tdType, align: center"]
Aircraft Type[/TH]
[TH="class: tdConfig, align: center"]Config[/TH]
[TH="class: dt-asc dt-sortable tdDD, align: center"]
Delivered[/TH]
[TH="class: tdPrevReg, align: center"]Prev. Reg[/TH]
[TH="class: tdRemark, align: center"]Remark[/TH]
[TH="class: dt-sortable tdName, align: center"]
Aircraft Name[/TH]
[TH="class: tdAge, align: center"]Age[/TH]
[TH="class: dt-last tdPhotoLink, align: center"][/TH]
[/TR]
[TR="class: dt-odd, bgcolor: #FFFFFF"]
[TD="class: nowrap dt-first, align: center"]VH-SDA[/TD]
[TD="align: center"]
482[/TD]
[TD="class: nowrap tdType"]
De Havilland Canada DHC-8-202 Dash 8[/TD]
[TD="class: nowrap, align: center"]Y36[/TD]
[TD="class: nowrap dt-asc, bgcolor: #EDF5FF, align: center"]19-04-1998[/TD]
[TD="class: nowrap, align: center"]
C-GFQL[/TD]
[TD="class: remark, align: center"]N482YV Mesa ntu[/TD]
[TD="class: nowrap, align: center"][/TD]
[TD="class: nowrap, align: center"]16.1 Years[/TD]
[TD="class: small dt-last, align: center"]

[/TD]
[/TR]
[TR="class: dt-even"]
[TD="class: nowrap dt-first, align: center"]VH-SDE[/TD]
[TD="align: center"]
453[/TD]
[TD="class: nowrap tdType"]
De Havilland Canada DHC-8-202Q Dash 8[/TD]
[TD="class: nowrap, align: center"]Y36[/TD]
[TD="class: nowrap dt-asc, bgcolor: #DBEAFF, align: center"]05-10-2001[/TD]
[TD="class: nowrap, align: center"]N453DS[/TD]
[TD="class: remark, align: center"][/TD]
[TD="class: nowrap, align: center"][/TD]
[TD="class: nowrap, align: center"]16.2 Years[/TD]
[TD="class: small dt-last, align: center"]

[/TD]
[/TR]
[TR="class: dt-odd, bgcolor: #FFFFFF"]
[TD="class: nowrap dt-first, align: center"]VH-SBG[/TD]
[TD="align: center"]
575[/TD]
[TD="class: nowrap tdType"]
De Havilland Canada DHC-8-315Q Dash 8[/TD]
[TD="class: nowrap, align: center"]Y50[/TD]
[TD="class: nowrap dt-asc, bgcolor: #EDF5FF, align: center"]28-10-2001[/TD]
[TD="class: nowrap, align: center"]
C-GSAH[/TD]
[TD="class: remark, align: center"][/TD]
[TD="class: nowrap, align: center"][/TD]
[TD="class: nowrap, align: center"]12 Years[/TD]
[TD="class: small dt-last, align: center"]

[/TD]
[/TR]
[TR="class: dt-even"]
[TD="class: nowrap dt-first, align: center"]VH-SBV[/TD]
[TD="align: center"]
595[/TD]
[TD="class: nowrap tdType"]
De Havilland Canada DHC-8-315Q Dash 8[/TD]
[TD="class: nowrap, align: center"]Y50[/TD]
[TD="class: nowrap dt-asc, bgcolor: #DBEAFF, align: center"]17-06-2003[/TD]
[TD="class: nowrap, align: center"]
C-GIHK[/TD]
[TD="class: remark, align: center"][/TD]
[TD="class: nowrap, align: center"][/TD]
[TD="class: nowrap, align: center"]10.3 Years[/TD]
[TD="class: small dt-last, align: center"]

[/TD]
[/TR]
[TR="class: dt-odd, bgcolor: #FFFFFF"]
[TD="class: nowrap dt-first, align: center"]VH-SCE[/TD]
[TD="align: center"]
602[/TD]
[TD="class: nowrap tdType"]
De Havilland Canada DHC-8-315Q Dash 8[/TD]
[TD="class: nowrap, align: center"]Y50[/TD]
[TD="class: nowrap dt-asc, bgcolor: #EDF5FF, align: center"]27-04-2004[/TD]
[TD="class: nowrap, align: center"]
C-GZPP[/TD]
[TD="class: remark, align: center"][/TD]
[TD="class: nowrap, align: center"][/TD]
[TD="class: nowrap, align: center"]9 Years[/TD]
[TD="class: small dt-last, align: center"]

[/TD]
[/TR]
[/TABLE]