When my son started pre-school, we didn't even have the option of "a few days in summer." But I can tell you that the hardest thing I ever did was leave him at school that first day...and second day...and third...it got better after that, but I admit that when your child is clinging to your leg and screaming, it's hard to go. You just have to steel yourself and do it anyway -- your daughter will survive, I promise, and will probably calm down right away after you leave, and after three or four days, won't scream anymore. And starting her for a few days "to get used to it" before September will not guarantee that she still won't scream and cling to you when the regular school year starts anyway, especially when she sees and hears other kids screaming. Well, at least she won't be alone in that, right? ;) You might actually be better off just starting in September, when there will be other new kids and other crying kids. It's going to be hard anyway to leave her..but don't set yourself up for disaster.
I should also point out that no matter what you do, you'll definitely have it easier than I did...my son's second day of school ever in his life was 9/11 -- in New York City -- and I got stuck in NJ when they closed the bridges and tunnels and didn't get home for 24 hours. No matter what you decide to do, I guarantee you will in all likelihood get back there when you say you will and your daughter will be fine! And if my son lived through that and wasn't traumatized for life at 2 1/2, then your daughter certainly will! :)