We've been doing Easter in Disney for many years, and plan to again this year! When the kids were younger, I always packed some things from home but then also bought some specialty items in Disney. One time I found Disney Vera bags here at home and brought them to Disney to use as the "baskets." That was a super easy year because I pre-stuffed the bags at home and then just hid them in my luggage. All I had to do was buy a few trinkets in Disney and stuff them in the bags.
Another year, I used a couple of simple drawstring bags as the Easter baskets (again, I brought from home). My kids ended up taking those bags to water parks, so they did get use afterward!
Another time, we were at the BC and they had tables set up outside of the store where they were putting together baskets with the tight plastic over them. It was a little pricy, but it was fun to pick out a bunch of items in the store and then just give the CM to put it all together. The only hard part was hiding them in our room the night before. They offered to deliver them Easter morning and I probably should've done that.
As my kids got older (girls), we stayed at the GF and I went in the gift stores there and bought a bunch of stuff (bath bombs, soap, etc.) and the store had very pretty pastel-colored bags that they wrapped nicely with a bow and I used those as "Easter baskets"! That was fun too. I picked up some earrings and other little things too and added them to the bags.