My girl also has the same problem..she's 19 months old now! and I'm still very headache about this!
I had consulted doctor and do whatever they said, but not very helpful! my girl need to take a very very mild laxative everytime to soften her poo poo...but just help a little bit!
I recently used "rice water" to make milk every day, and cook 2 times "seven star tea" to make milk..seems work a bit! at least her poo poo softens, you can try try!
My mom also tells me to give her papaya every morning, it works! but my girl hates papaya..so it's hard to feed her!
Try prune too if she likes to eat.
Try baby yogult.It is the only method to treat my baby's constipation.My experience is that if baby can't pass boo boo daily, it will become hard even take a lot of water or fruit. So I will massage my baby's tummy after taking meal(30 min later) to help her have the urge.My doctor told me not to allow her to pass boo boo every several days.Boo Boo will become bulky and hard.Also the intestine will lose elasticity afterwards.He asked me to give mild laxative if without boo boo for three days.