You can't tell before a battle whether or not a pet is rare quality. But, it appears that you can use hitpoints as a guide to know when a wild pet is rare. So, if we were to make a list of how many hitpoints each rare has when we catch it, we'll probably have a reference sheet that we can use. While you are fighting, you'll probably battle enough pets that you'll get an idea. This would be for those afraid, well what if the very first one I find is rare and I kill it?
These are the rares I have so far and how many hit points they had when caught.
If people are interested in adding their own, I'll check back laters and update the first post. You can use the armory to see the pets, but I'm not sure it will be helpful if the pet has been leveled.
• Fledgling Buzzard (4) 373
• Fire Beetle (13) 903
• Nether Faerie Dragon (11) 636