I have some experience with adult cat introductions- from my mom- who introduced Cindy to her brood. My oldest cat has been 1.5 or so years, and that was Minnie, the feral. That prolly isn't an appropriate comparison.

First, I personally think a week is WAY too early. Far better to move WAY too slowly than completely ruin an introduction. I would go a minimum of 3 weeks- no cheating. Once you ruin it, it is virtually impossible to come back from that.

Do lots of switches of bedding/towels/scents, etc. It is great if you can switch out rooms, too. Put all your regulars in the spare room, and allow the new cat to have free roam.

Finally, 30 days is not enough time to allow the allergies to stop. I heard just the other day it takes 3 months to get rid of the dander, and that is with ramped up vacuuming. I am not a big proponent of "I think I am allergic to cats". I would get tested. I don't know how old the baby is- but I know enough about children and doctors to know one of the first things probably said were, "do you have cats"? Maybe the baby is allergic...but, maybe not. I was told my child had allergies for months and months and months. I knew he wasn't...and it took the allergy test to prove it. STILL the ped would mention allergies, and I politely reminded him there were none.

Good luck.