We have a son, age 7, with Type 1 also. He is now on a pump but here are some different things I did.
For a while, I carried an insulated lunch box that I purchased from Lands End and carried ice packs in it to keep it cold. I was also able to keep juice and other snacks cool.
On later visists, I carried a case I purchased from
www.fifty50.com made of neoprene. You can purchase a gel cool pack with these and it seems to work ok, too. This carrying case opens up so that it is easy to get through security.
I also used a small soft cooler about the size of a camera case made by Safety First. I found it in the baby section at Wal-Mart and it's original purpose was to keep medicine cool. It came with a gel pack, too. Since you can't refreeze things on site, we used ice in Ziplocks and wrapped the ice pack in paper towels in case it leaked. This fit easily in a backpack and wasn't as cumbersome as the lunchbox.
When I stored insulin at the nurses station, I felt like it was a pain to walk over, get the insulin, go to dinner, return the insulin, stop back by before I left the park..... One nite, I forgot to go by the nurses station to get it! Luckily I had a spare bottle in the room.
I agree with Ambassador. The Kid's Meal choices aren't great for kids with diabetes so don't be afraid to ask for a grilled piece of meat. I like to carry a Peanut Butter sandwich and piece of fruit, too, just in case. We usually see pretty high blood sugars while we are at WDW.