We were in Magic Kingdom the Friday before Memorial Day last
year, and it was pretty crowded. AK on Saturday was crowded too, but I don't remember Sunday in Epcot being tooooo bad.
The first weekend of June has traditionally been gay weekend the past couple of years. I've read on these boards, (not personally seen) that there is some outward affection displayed. If this would be a issue, then you might want to know this. Your child might be too young to notice or old enough to not care! It's a personal decision of when to visit WDW.
Have fun!