In my experience, they are very up to date. You'll have a choice of Hamad--which has vaccination centers around town and a number of private hospitals and clinics. They'll issue you a vaccination card when your child first sees them so as to ensure that you have your own record. I would suggest bringing your vaccination records with you so that they don't try and double up. Flu vaccines also run bit later here than in Europe, due to the later onset of winter.