According to Nemours Kid’s Health, mosquito repellents that contain DEET are safe for use on babies as long as:
The kids are 2 months and older. It is applied once per day. Not applied on the face, hands, near the mouth, and irritated skin of the baby. Not more than 30% concentrations.
Make sure to wash your baby’s skin as soon as you arrive home to remove the residue of repellent on their skin.