Well, my kids help alot around the house. It's not so much a time issue as it is a space issue. Especially with all the twins equipment, two highchairs, two walkers, going to be setting up two toddler beds in a few months(we only have one crib, they love sleeping next to each other) We feel like we have room for one more kitty, but just couldn't fit anymore in here! Ok, well the cat would fit but the extra stuff wouldn't.
From the kitty point of view I can't really help you much. My cat is the first cat I've ever owned! From the kid/mommy standpoint: You might want to wait until you're daughter is better about not kicking. She could really hurt a kitten by accident without meaning to and that would be heartbreaking for both of you. The two month old isn't going to really care either way
but lemme tell ya, I've rescued Simon(my kitty) from Charlie's version of "loving" on him more than once. Charlie is enchanted by Simon's tail and seems positive it must taste good. He's never had a chance to find out, as I'm on guard every time they're in the same room together. Funny thing is Simon just keeps going back for more, Charlie will grab him, I'll rescue him and five minutes later he's back rubbing on him. Samantha(Charlie's twin) is much gentler and is content to have Simon rub on her without grabbing him.