I can't come up with anywhere in Wappingers Falls that deals solely with pediatrics. When I think of pediatrics around here, I think of Children's Medical Group up in Arlington right by Vassar College, which is where I went. There's another CMG location off of Route 9 in Fishkill by the Wendy's before you get to the Wal-Mart plaza.
The medical options in Wappingers Falls are some specialists (like a chiropractor on Route 9) and places like Hudson Valley Primary Care and the walk-in clinic that used to be called Medicus but I believe changed its name.