I think my cat cured me of seasonal allergies. I used to have a little bit of a reaction to cat scratches (the area would get puffy and swell), and occasionally I'll get that reaction, but other than that I don't seem to get bothered much. I used to get horrible ragweed alleriges, insanely itchy roof of mouth, sneezing, headache, stuffed runny nose, just miserable, and since I got my cat I've yet to feel any of those symptoms. Wierd huh?
The danger of getting a cat if you know you have an allergic reaction to them is that you might develope a "fatal reaction". Some people are so allergic to certain allergens, it makes them go into shock and can end up dying (bee stings, cats sometimes, jellyfish stings, etc). Do you have a friend that has a cat? Maybe you can try "hanging out" with a friend's cat for a bit and see just how bad the allergies can get. Or go to an animal shelter and play with their cats for a bit.
Problem with cat allergens in particular is that they are HARD to wash away. The allergen responsible for cat allergies is a protein in their saliva, not their fur. The other problem is that these proteins are polarized, and it makes them extremely "sticky". So even if you do use filters and vacuum religiously, the amount of allergen will build up over time, and if you do decide to get rid of the cat after the fact, it could take months if not years before all the allergens fly away.
Are your floors at home hard floor or carpet? If you have carpet, could you make the investment to change it to hardwood type flooring? Hardwood flooring is much easier to clean and you can get some of the allergen off by moping. Carpet seems to hold it in and collect it over time.
Another option would be to get a pet you're not allergic to. Ferrets are great, since people rarely have allergies to them (they're considered hypoallergenic pets), but they're not as cuddly, and more "troublesome" (really kinda depends on what you consider troublesome). They're kinda like cats... mm... like a perpetual kitten, high energy, high maintenance.