it's a long drive.
we just drove down from nowra area (below Wollongong) to melbourne. it was one of those super hot days in early january too. took us a good 10 hours once you factor in all the toilet breaks etc. and you are totally exhausted by the end of it.
i would start looking at car hire/baby seat hire options if i were you.
(darn lack of multi-quote on tapatalk!)

That's what I'm worried about - that it'll take hours and we'll be completely wrecked before we even get there.

Maybe FIL could drive up and get us from Sydney. I don't think they could take car seats up for us but possibly we could take car seats on the plane...

Might need to google cheap accommodation ideas...