The parks are opened longer to compensate for crowds in the summer, and if you stay on site, you can take advantage of EE mornings, and on other days, just be there when the gates open, because the crowds are much less dense in the first hour or 2--- a WDW vacation in the summer, Christmas and Spring Break is not the time to lounge in the bed in the morning... or plan elaborate early morning character breakfasts... the early bird most definitely gets the worm, in this case. Fastpasses are a great help, as well.
Usually mid June through mid July are relatively crowded, but it definitely depends on your opinion of crowded... if you are comparing it with the time between Thanksgiving and mid December, yes, it will be crowded.
We have found that by waiting until the 2nd week of August, we can avoid many crowds, but in return, we have rain.
I think you will be fine... personally, I am hoping that the attendance picks up by then, not to slight you, but attendance figures are down, so unless we want to see them start cutting things like they did after 9/11 we should all be hoping and praying for the same thing!