It all depends on the person. I have a 14 month old, I left his father right before he turned 2 months, and have not dated since- nor do I plan to for a while. I am not ready to put myself through that again. I am happy just concentrating on me and my DS for the time.
There may be someone else on here in my situation- young toddler, left ex a year or so ago- that is ready to date. More power to them and I wish them the best of luck. Only YOU know when you are ready to date. If you "keep pushing them away", as you say you are, you might want to sit down and really think about your life and what you want. It could be your bodies way of telling you to slow down and concentrate on something else for a while. I believe you're 20, right? You still have plenty of time left for dating!