How Long After a Tummy Tuck Can I Take Care of my 4 Month Old Baby?

As long as you want but probably at least 17 years and 8 months! However, speaking as a father of four...it can be even longer!!! But I don't think that was really your question...I tell my patients to plan on having some help around the house for at least 10-14 days and no heavy lifting for 6 weeks, not much of a problem with a 4 month old...But be careful. I'm still trying to "lift" my 21 year old out of the house....

Thank you for the question.
As you know the tummy tuck operation is a major operation;  every patient experiences a different recovery course. This makes it difficult to discuss “general rules of thumb”.
I would suggest planning for the worst-case scenario which will hopefully be about 4-6 weeks away from child care activities. Your  plastic surgeon will help guide you  with activity level depending on how your recovery proceeds.
I hope this, and the attached link, helps.

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.