Is he going to ask me to marry him on my birthday?

A dream is your body's way of telling you of the things that are in your subconscious. You obviously want to get engaged, and your dream has been created around that thought. I can't say for sure if he wants to get engaged - has he ever said that he'd like to be married one day, mentioned having kids of his own, etc? If not, then theres probably a good chance he won't be proposing any time soon. If you think he is the marrying type - then just be patient - if it's meant to be then it will happen. Your dream won't have any influence on his decision.