I think you would be fine with just having that open but ya know when it gets cold you will want one because the girls probably wont want to go outside anyway I don't have a door on the coop part of mine for the chickens and they hate going outside in the winter so i figure I just lock them up...
It is very nice! but with the brooder at a time when the chicks start making a whole bunch of dust I am afraid you might have a small problem there, because it is so open. but like i said you did a good job on it!!!