It's really a matter of whether you're allergic to animal dander and fur. Another thing to consider is if you're going to have a pet that is indoor AND outdoor, you might have more trouble with allergies. Remember that our furry friends will track in just about everything with them...dirt, mold, spores, pollen, even other bugs.
If you'd like to get a pet, be sure to do your research. Don't be fooled by the so-called "hypo-allergenic" pets. No such thing exists; but there are certain breeds that are better than others for people with asthma, allergies and CF.
I have had no problems whatsoever with my rabbit, Gimli. He doesn't shed, instead he molts. The only difficulty I've had is with the food I give him. I've had to switch to a brand of hay that doesn't irritate my allergies as much.
Be sure to get a good HEPA filter that will deal with pollen, dander, etc. that your pet may put into the air. Also, the Cystic Fibrosis Foundation has recently recognized Febreeze as an effective product for cutting down on allergens.
Want to read a bit more? Here are some links: (personally, I think the first one is a little sappy)
<a target=_blank class=ftalternatingbarlinklarge href="http://www.thisislancashire.co.uk/news/headlines/display.var.1899192.0.melanies_new_pup_is_not_just_for_christmas.php">Puppy as a Gift to Girl with CF</a>
<a target=_blank class=ftalternatingbarlinklarge href="http://www.helium.com/tm/114846/asthmatics-often-discouraed-keeping">Pets and Asthmatics</a>
<a target=_blank class=ftalternatingbarlinklarge href="http://www.helium.com/tm/111366/asthma-preventable-highly-treatable">Taking Precautions Against Asthma</a>
<a target=_blank class=ftalternatingbarlinklarge href="http://www.helium.com/tm/114214/exotic-often-misapplied-animals">Brief Guide to Laws about Exotic Pets</a>