Most patients require narcotic pain medication for 3-6 days after a tummy tuck. They need to walk bent at the waist to take pressure off of the suture line for about 1 week. After that, patients are sore, but not in pain for another week or so. I place limitations on my patients in terms of heaving lifting. A four month old is not heavy enough to be considered heavy lifting and you should be able to hold and take care of her without much issues as early as 1-2 weeks after surgery. There are other day to day activities that might be more limited than the daily care of an infant.
On a different note, I typically tell my patients to wait for at least 6 months after delivery before considering an abdominoplasty, and actually prefer for them to be about 9-12 months out.