Yes, perfectly normal for her age! It will pass. Here are some strategies I've used with varying success:
Matter of fact tone of voice, "Oh, I'm sorry, had you wanted to open the door by yourself? I didn't know that. Next time I'll try to remember that it is your turn."
"You wanted to open the door yourself. I hear that you are dissapointed. You sound very frustrated."
With those 2 strategies, I might give him a chance to go back and do it over. But generally I just keep walking as if the situation has been resolved. He might wimper a little, but if I succeed in sounding unfrazled and matter of fact -- he usually concedes.
On the other hand -- I don't see it as a big deal if he wants to go back and open and close the door over again. Its only a minute out of our day, you know?
"Feel free to open the door for yourself. I would like to open it for myself this time."
"Thank you for trying to be a big helper. I usually love having help. But today I would like a turn to do it *my*self! Even though I am big, sometimes I like to do things myself too! Remind me next time that it is your turn."
I also work hard on teaching my kids that its okay to ask for help. I do this by giving positive feedback when they do. "Great problem solving! You asked for help, which is a great way to get something done."