I've written an article on the main site about introducing your pets to your baby, have a look there

Also, the screen door is a good idea, as long as it doesn't squeek!! Imagine putting your baby blissfully in bed & then opening the door to the squeek waking them up! Eeekkkkk can't think of anything worse.

One thing that I found worked really well for some people is setting the cot up & wrapping the mattress in aluminum foil because cats hate jumping on that. Also buying some pheramone spray from your local vet to help calm the cats in that area. Spray the cot & pram with it. Anyway... have a read Pets and Your Baby - Preparing Your Pet For A Baby