Thinking about dating while pregnant.

i am 19 years old, i am 3 1/2 months pregnant with my first child, i was with my child's father for about 5 months when my birth control failed on us. before i found out i was pregnant my feelings for my boyfriend went south, i was really considering breaking up with him... and then i found out i was pregnant and things went even more down hill. after dealing with not wanting to be with him for about another month i finally broke up with him. but after being single and pregnant for a little over a month now im realizing i want someone to share this experience with. i met a man a week ago and things are going very well, i am taking things very slow with him and he seems fine with the fact that i am pregnant. my concern is that my child's father is still involved (being at doctors appointments ect) and i dont know how to bring this up to him or anyone else, that im considering dating someone else. i mentioned it to my sister and she thought that it was "disgusting" that i would be considering being with someone while im pregnant with someone else's child. i need to know how other people feel about this situation and how i should deal with telling people that i may be ready to date again and once (if) i start dating someone how to answer the question that im most concerned about being constantly asked "what man is the baby's father?". so if someone could please help answer my questions and give me advice on the subject it would be greatly appreciated.