The cat is annoying me - don't want him near baby

Gi

I have a cat who sheds like a mofo and who loves to stink up the house. It's INFURIATING, and even more now that I have a baby. When my baby starts crawling, I just know he's gonna end up finding a clump of fur and putting it in his mouth. I have to keep the cat in a room most of the day because I don't want him on the baby or on his clothes or toys or anything that can end up making contact with him. I only let him on one cushion of the couch when he is out of the room - the furthest one where baby and I sit. I am somewhat allergic to the cat - it's a lot better but I still itch when his drool comes in contact with my skin. I don't want any of that around my baby. I really just wanna get rid of the stupid cat.

My mother-in-law says that she hears about parents struggling with babies and pets. My cousin even says how she wishes her cats would just run away already. She used to be so in love with her cats like me, but now that we have babies we just find them annoying and want them gone. My husband wants to keep the dumb cat though. Who else has an annoying pet and doesn't want them near the baby?