at the end of the day if re-homing is the only option that makes you feel comfortable then go with it.

that said, we have 2 cats and a dog (and a baby!). if there is a sliver of a chance of you keeping the cat then do some research into how to find house-harmony for your pets and new baby. we spoke to our local vet who gave us HEAPS of great tips for the transition.

some included: letting the animals explore the nursery BEFORE bubs arrives. then, close the door and that's it. out of bounds.

get DP to bring back bubs clothes and your clothes from hossy so that they can smell it and get him to put them in the nursery and let cat sniff it in there.

at night, we put the cats in the spare room and closed the door. they had their water and tray and were happy as larry (in fact i think they were relieved to be away from the screaming, pooping machine LOL!).

true, you need to be vigilant and let the cat know that you are TC (top cat LOL!). and that baby and baby's things are off limits. water in a spray bottle may be your best friend for a week .
BUT, the reward of pets for kids is also amazing. and so so quickly cats (and other pets) begin to see the new one as part of the group and harmony is achieved again. our cats NEVER show interest in DDs room and have NEVER scratched her as a young baby...one gave her a swat when she pulled his tail but the claws were sheathed and that was only a couple of months ago (DD is almost 2). in fact we found they largely avoided her. were a bit perplexed as to why we went and brought home such a loud and hairless beast LOL!