For future chick purchases, you can purchase power inverters that will power most things, including a brooder. We had to drive at least an hour and a half with chicks that were a few days old and they all did great with the brooder + being given water at least once an hour.
Hi! Welcome to BYC and keeping quail. I only recently started keeping quail myself (now going on...3 months?) so I would defer to any more experienced keepers. I'll try to answer a couple of questions, though.
Firstly, it would be best to have pictures of your set up and what you're feeding...