The real issue is that for $400-$600 you're not going to get anything much better than your current camera. For that price you can maybe squeak by with a new entry level camera with an 18-55 variable aperture kit lens or a used mid range with some crappy (and by crappy, I mean the image quality is terrible) 70-300 variable aperture lens.
The problem is, that $400-$600 you're spending on the camera will barely eek out a lens good enough to do wildlife photography if you're looking for quality. Variable aperture zooms nearly all have a pretty terrible IQ compared to a single maximum aperture zoom. The difference is, for a cheap 70-200 f/4L from Canon, you're looking at about $500 used. 200mm is still short for wildlife if you want any close photos. A lot of people that need a decent quality zoom go with something like the Canon 100-400 f/4.5-5.6L IS and you're looking at about $1,600 for that lens or they go with the 400 f/5.6L telephoto prime for about $1,350. If you think that's expensive, the 400 f/4 IS will run you about $6,500.
Lenses are one of the number one pieces of gear a wildlife photographer will depend on and will make a huge difference in which one(s) you use vs. which camera body you go with.