I don't see why you wouldn't qualify with your scores and modest price of that car and your income.. Asked for it to be moved to auto section of forum. I would suggest DCU or PenFed or using a CU for a really good used car rate as well
You should be good to go from a financing standpoint.
You may want to check out Cargurus.com and Carmax.com to see what similar cars like the Avalon you are looking at are being sold for in your area.
PenFed is one of my favorites as one EQ pull can net you multiple products if you are in the market.
Good luck and let us know how it goes...