I get allergies to some animals, unfortunately i LOVE animals:( When i get allergic, i get hives, asthma, watery eyes, and a stuffy nose. your daughters allergy sounds like heaven compared to what I go through. LOL. Honestly, with such a mild allergy, I'd keep the dog and go from there.
Having allergies, I have found through research and conversation that is is quite common to have an allergy to a specific animal reduced by just getting the body used to it. If anything, your daughter's allergy to the dog should lessen as the months/years go by. I also have found on my worst allergy days, a Zyrtec is helpful- it just makes me slightly sleepy. Another thing to possibly consider is allergy shots, but i think that should be for more serious allergies... One thing you can do often is bathe the dog with a mild soap (as not to irritate the dog) frequently. This keeps the dander at bay a bit. also, I'd keep the dog away from her room, always. Let her room be an off-limits place for the dog.
My daughter also has allergies, but our main concern was her asthmatic reaction to things and we have her on control medicine that works wonders. If she shows allergies in any other way (we don't have any animals in the house she is allergic to, though), she just deals with it the good ole fashioned way with tissues or if it gets bad, Zyrtec. That is NOT often at all, though....
Honestly, I would not worry too much about the mild allergy, but there are measures you can take to help...