I've been "back scratch" tested for allergies. Can the doctors do a allergy tests for specific types of dogs?

No. There is no commercially available tests for specific breeds of dogs. You can be allergic to a common shared allergen, a breed specific allergen, or both. Unfortunately, the currently available testing material is for mixed breeds as well as the common shared allergen and not available seperately.
No. Usually the scratch test (back or arms) includes a test for dog--there aren't reliable tests for different species.
Maybe. Dog allergy is typically due to a common allergen among all species, but your immune system may pick up small differences between species. Your allergist can make a crude extract from skin scrapings from a particular dog, but it's just that - crude. A positive skin test will mean that you're allergic to the dog, but a negative skin test with a crude extract doesn't rule out allergy.

Related Questions

I've been "back scratch" tested for allergies. Can the doctors do a allergy tests for specific types?

See below. The scratch test does test for specific allergies. Blood work can also be requested for allergies. However, most allergist believe the skin testing is more accurate.