My daughter was given watered down & then straight prune juice at about the same age for the same problem, it took time but worked. Although until she was about 3 we still had to give it to her regularly & sometimes had to use a suppository (script from dr) as in her case the problem was that the muscles at the "mouth" of the anus just didn't(& don't - she's 15) work properly.

You might consider if bottle fed trying a different formula (non-dairy?) or if breast fed then it may be something the mum has that the baby doesn't like.

Also some children need fibre (solids) sooner than others my son started on solids at 2 weeks of age. My daughter at about 8 weeks.

My daughter was constipated when we started her on formula. We had her on the powdered, but that was actually the culprit. The doctor had us switch to liquid formula...Either ready made or concentrate. It reall really helped. Also, adding some kayro syrup to the bottle helps....As does warm baths to help relax the muscles, and very gently stimulating the muscles by inserting a thermometer up her bottom....Very gently and very little. Good luck