DisneyLAND is VERY lenient about bringing in food. We bring in food about 50% of the time for our little ones (no special diets or medical needs, just picky eaters!). Never an issue. We use soft sided insulated bags, though.
However, no ROLLING coolers are allowed. If you can keep it to a small cooler, no one will mess with you about it.
If you need to keep insulin cool, you can use the First Aid center in either park.
If anyone asks you about the food, a simple declaration that your daughter is Type 1 diabetic will suffice. You don't need to have any proof. But, as I said, they won't bother you, unless it looks like you're trying to haul in enough food to feed a family of six...
You will also find a LOT of healthy snack food items around Disneyland Resort. Much more than you see at WDW. Gotta be the California consciousness thing with the health.
Some places to keep in mind:
Disneyland park:
Main St. Bakery (fresh sandwiches), no sugar added desserts
Fruit cart on Main Street
Fruit cart in Adventureland
Toon Up Treats in Toontown
These three places, in addition to having fresh whole fruit, also offer cut up veggies and dips, cut up fruit, fruit cups, granola bar/power bar type snacks, yogurt parfaits, trail mix, etc. They have these things called "Foodles" for kids, which are little trays containing either fruits or veggies, a cracker of some sort, and a dip. They come in three varieties.
In DCA:
Bakery (sandwiches), as well as no sugar added desserts
Fairfax Market has a similar fruit stand
In the resorts:
White Water Snacks at the Grand Californian is the most easily accessible CS location from either park or Downtown Disney. You don't have to be staying there to use the entrance from DCA into the Grand. Just walk in. The restaurant is located by the pool area. LOTS of good options in there, in the refrigerated section.
At Downtown Disney:
Jamba Juice (for smoothies and fruit & vegetable juices), oatmeal for breakfast in the morning, and they now have salads and WRAPS (good ones!) for purchase all day in a refrigerated case. Their baked goods are also healthy. A few no sugar added or low sugar options, both in the smoothie menu and baked goods menu.