I've always needed ID, even for a minor.
The airline might not check it but they'll check it going through security. I *think* a copy will work but I'd call the airline to make sure.
We all laughed and I said "No, I think she'd like to know you're name." My daughter was so embarassed.I hadn't realized you may be asking since the 4 month old could be on your lap! Although SW may ask for one, a 4 month old is very obviously under 2 years, so you will not need one.
At WDW, the 2.5 year old also will not need one. They take your word for it that your child is under 3, and doesn't need a ticket.
So you don't need anything in your case.
