Since you say that you are really ready for a serious relationship, then why are you feeling unsure? How come you feel the need to allow others to dictate to you on your actions? Others aren't living in your skin, so how can they presume to tell you how to live?
There are no rules about how soon is too soon to start over. All that matters is that you are listening to your heart and making good decisions for yourself--not for your friends--for yourself.
Is it possible that you are hiding behind your friends' doubts? That is, do you have doubts of your own that you are afraid to admit to yourself? Are your friends merely voicing your own secret doubts? Are you afraid that this man will cheat on you like the last one did? Examine this question, and if you find that you still feel clear and ready, then follow your heart.
If you decide to become more serious with this man, I wish you every happiness.