Dear S.,
What a shame that your daughter is allergic to dogs!
Wheat is known to cause allergic reactions, even to other allergens, to increase. If your daughter's allergies are somewhat manageable, you could try withholding wheat from her diet to see how she does. Dairy is also a culprit here, since dairy is known to cause congestion. Try Ezekiel bread instead of standard breads, and soy or almond milk in place of dairy.
About a year and a half ago, I stopped eating all dairy and grains (except oats) and it has made a huge difference in my allergic reactions.
It's the animal's dander and saliva that contain allergens, so you should vacuum frequently with a hepa filter if possible. Try to keep the dog out of your daughter's room to reduce allergens in her environment. Febreeze makes an excellent allergen reducing spray, too.
Just yesterday I received an e-mail with great tips for reducing pet allergens in the home, so I'm going to go search for it to see if I can send you a link.
Good luck! It would be terrible if you had to re-home your best friend!
I just found this wonderful link that you might find interesting:
http://www.care2.com/greenliving/the-benefits-of-pets-for...