Huwcar
It may be worth doing it through a travel agent rather than myself online if it will offer some protection.
What protection? This is the last thing I would be doing as you cannot assume the booking will all be on the one ticket. They may book it separately as two tickets just like you were going to the only difference being you will have paid the travel agent a hansome booking fee for the 'privilege'!
Also when you book through an agent, in a disrupt situation the airline may try to 'handball' you back to your travel agent if there's a 3rd party involved and I would question how helpful that agent may be at 0300 on a Sunday particularly if it's a certain chain I'm thinking about.
If you've booked direct with the airline they can't flick you or fob you off and must take care of you. The more budget the airline the less likely the chance of them transferring you to another airlines flight though.
Not sure what city you're in but ex DRW a quick check of the JQ website shows JQ57 DRW/SIN 1600/1900 on 13May returning 20May JQ62 2220/0430+1 costing AUD339.81 return per adult including taxes.
If it was me I would book a cheapie JQ fare online myself ex DRW to SIN for example, overnight in SIN both ways then do your separate fare on whatever airline ex SIN to LON or Europe. It may be worth checking cheap fares ex your capital city to Darwin & departing from there.
That eliminates any worry of a)missed connections due to flight delays and b) no need to claim baggage & recheck as you'd be overnighting each way.
Good luck with all the planning & let us know what you end up doing.
Cheers
Oz