I would get a full workup done. A typical grass/mold/pollen allergy are typically on the underside of the dog- feet, belly, etc. It's hard to say what's going on especially if we can't see the dog. Maybe you could post a picture?

I would ask for (if they haven't done it already) a skin scrape to rule out mange, a once over with the wood's lamp (blacklight) to show if it is a fungus, and then maybe a fungasay test, where they pull the hair and stick in a bottle and see if it changes colors (would show fungus). Unless the doc is sure it's allergies. Some vets just assume its allergies without any other diagnostics. Provided you rule those out, then maybe allergy testing. It sounds like the doc thinks its an outdoor allergy and not a food allergy. Maybe try putting a dog jacket on her when she goes out, see if that helps. Anyways, if you could get some pictures that would be great. Best of luck!