I have been to Turkey a dozen times and have never had injections, because it is so westernised now - not like it used to be.
I just take malaria tablets (Avoclor from Boots chemist - very cheap), which I think are ok for children also, but check when you buy them. You take them 2 weeks before you go, the time you are there and then 2 weeks after you come home.
Take plenty of mosquito repellent and also be prepared to get "Turkey tummy", because no matter how careful you are with bottled water etc, when you eat out, it can still get you! The pharmacies are very helpful, you're usually given yellow tablets and they will also advise on what to give the children.