Hi Sam and welcome to Myswag...you've really come to the right place!
The guys have given you all great advice and probably your head is buzzing already!
Single mum here as well but with an older teenager now and we've been having adventures in the camper for about 12 months now. So, still far from being an expert but have definite ideas on some things! I have a Hilux 4wd to tow my camper with. As where I live out here there are plenty of dirt roads you travel on just everyday, it suits me for that purpose as well but like you, I'd probably not go off 4wding by myself. However, having friends with 4wds means I can go with others on those style of trips as well. Even having met people from this forum who are keen 4wders has got me out off the black top as well.
Having said that, I don't want to make you have upgraditis but at least have a look at a map of Australia and see just how little of it is serviced by bitumen roads as compared to dirt roads. I agree with the guys advising you to have a look at the small SUV's as you might find that even they will handle our worst bitumen roads better than the station wagon and pretty much all of them are just like a small car to drive.
If you are going to stick with the Camry, make sure that if you decide to push the 1300kg towing capacity, you at least have some sort of brakes on the camper. In fact, I think in most states if your trailer is over 750kg in weight, it must have brakes.
Good luck with your search and all the best for your big adventure!