Buy a good vacuum with a premium HEPA filter. It'll cost some bucks but it's worth it.
Give the house a good reaming out. Use your new vacuum on all carpet and fabric surfaces, clean the rest of the surfaces until they shine.
Have the cat bathed and thoroughly groomed while the house is being done, then buy a comb & brush for her and keep up with daily combing/brushing.
Purchase some cat wipes in your local pet store. They are special wipes made to absorb cat dander and do wonders for people with allergies.

With a bit of work, it is possible to live quite easily with a cat even if you have allergies. I live with a violent allergy, asthma and sixteen cats just fine.