Yes, they have allergy tests for dogs. I think you can get more simple ones though, like blood tests (I think those are just for figuring out if the allergies are food induced or air induced or whatnot though). You might want to ask Cincy's Mom; I hope I'm correct that Cincy has had some allergy tests before.

What type of food is Jasper on? If you think he has food allergies, you might want to eliminate any foods with corn, wheat, beef, or chicken in them. See if he still has allergies after that.