My doc put me on a 1200 cal diet and strict exercise routine. I am losing all my fat but my baby fat. How can I lose this as well?

keep going! Keep going, follow the doc's instructions, you will lose this eventually as well. Good job!
High stress hormones. Having more stress hormones like cortisol can prevent people from losing fat around belly button. In this case reducing stress and practicing relaxation breathing or guided imagery for 5-10 minutes twice a day can change fat loss pattern. One set of symptoms characteristic of too much stress is having trouble going to sleep at night and trouble waking up in the morning.