I have a private database on all of the cash components, including carrier charges and taxes. I'm not aware of a sytematic approach to extract this information, and it does change from time to time. However, this information can be checked by looking it up per route. That is, if you can find availability. I will share a few insights, however.
There are a few notable carriers which charge outrageously expensive carrier charges for QANTAS Frequent Flyer members. Those are Qatar (maybe because of the bad relationship since being denied routes to Australia) and Emirates. In my opinion, the value is so bad that it's pointless to book these carriers.
Another one to consider is Jetstar's carrier charges from coughet to Sydney in economy is $95 one-way. Jetstar's Bangkok to Melbourne in economy is $85 one-way. That really puts a dampener on value.
On QANTAS, SYD-DFW or PER-LHR are $140 in carrier charges in economy one-way. That's if you're somehow flexible enough, and can even find availability almost a year in advance.
I wouldn't recommend mixing carriers, if you can avoid it. It's usually terrible value.
