I think the dog would be safe enough in the front footwell. As long as she doesn't move. Mine wouldn't budge from where I put her. Even now, she's only just brave enough to sit up and look out but mostly she sits pancaked on the back seat (with a harness on).
I suppose it's a toss up between the risk of rolling the car or the risk of her getting a bad doggy something in the next couple of weeks. I suppose if she's not visiting any areas where unvaccinated dogs or foxes might be - she could be ok. vetprodcutsdirect are pretty good and deliver to the post office. I also like vebo pets but they don't use australia post so that might be awkward.
I don't know if your area is bad for heart worm either - it depends a bit where the mozzies have been. some places have stuff all mozzies so there's stuff all risk.
It takes me an hour to get to my hockey games or RSPCA and an hour and a half to get to the AWL and 30 minutes plus to get to the vet where I get my dog's vax done. I suppose you'd be travelling at a higher average speed but the times are similar. Maybe phone the nearest vet and discuss risks and what you can do in the meantime to reduce them. You could also ask about call out fees - if they happen to have a call out for someone else in your area they might be able to sort something at a price you can afford.
The vax, wormers, flea spot ons and tick preventatives do tend to add up. I spend a bit over $200 per year on all that. And it's more expensive for puppy because you usually need more than one vax shot to get the dose set. Free puppies are not really free if you want to give them the best care. But vax are cheaper than a week in vet hospital with one of the diseases they prevent or reduce the severity of (kennel cough).
Some vets offer payment plans - though paying up front is always cheaper.