I'm not a fan of doing laundry on vacation, but for 9 days, you'll probably have to. If you decide to do laundry, you'll really only have to pack clothes for 5 or 6 days.
I've found that it's pretty warm in April, a little cooler in the evenings sometimes. We usually bring shorts & capris of the same color with at 2-3 shirts for each color.
We wear a zippered sweatshirt or light jacket on the plane & that's our jacket for the week. If you wear jeans on the plane (although I always wear shorts or capris) those are your pants for the week.
I always overpack - never fails - regardless of how hard I try not to, although I'm getting better.
Don't bring too many pairs of shoes - sneakers (worn on plane), sandals & flip flops are more then enough.
Must haves - over the counter medications, band-aids, etc. They are pricey in Disney & something we always end up needing.