A cat generally won't go near the baby...but to be safe just maybe put a mosquito net or something similar over the cot while the baby is fairly young cause once your infant starts crawling he/she will want to grab the cat all the time and therefore the cat will just want to stay away, maybe close the baby door while sleeping and just get a monitor instead. THere are plenty of ways if you want to keep your cat and have a family.
I agree with the toxoplasmosis...your DR probably just doesn't like cats and babies together. I certainly wouldn't get rid of my Birman cat....but i would be cautious!!