There is a risk of your child getting diabetes if you've had gestational diabetes.
Type 1 diabetes (often called childhood onset) usually does not cause obesity.
Type 2 diabetes (adult onset) is caused by a lifestyle of inactivity and obesity. However unlike Type 1 diabetes, it is TOTALLY reversible and controllable with lifestyle (exercise, loosing weight and eating healthfully). I doubt that your toddler is overweight enough to have this type of diabetes, though children CAN get it, they are usually older and severely overweight.
As far as her having something medically wrong with her, I'd say if weight gain is the only symptom, there probably is not. Focus on getting her to eat right and exercise and see what happens. If she's doing that, and still the weight piles on, then you should pursue a medical problem.
As far as watching her diet. First, she should not be eating refined carbohydrates like sugar, corn syrup, white flour (found in breads, pastas and prepackaged foods) etc in excess. Small amounts of these are fine, but unfortunately our American diet is full of this stuff, so its very easy to over do it. Look for whole grain cereals with no added sugar (cheerios - origional in yellow box, or corn, rice and wheat chex are GREAT options). Also limit the amount of milk, juice, soda, or coolaid she drinks. These are full of sugar! Eating fresh fruit is MUCH BETTER then drinking fruit juice, even if its 100% juice - which many are not. Learn to drink water! Soda is ONLY for a special treat. And always get whole wheat bread!!! Avoid things like pop tarts, chips, snacks in general. Anything in a crinkly bag basically. You don't want to eliminate carbohydrates as many people suggest, but eliminate processed/refined carbs and replace them with whole grains and legumes (beans).
Secondly avoid excess fats. Avoid fast food across the board. We all need fat in our diet, but try to limit the fats you add to foods. Be sure to buy lean meats, and don't add fat when cooking them. Try some soy meat substitutes to cut down on saturated fats! Especially if you want to serve things like hot dogs and nuggets, the soy ones are much healthier for her - though even they are not something she should eat daily. Keep dairy products to a minimum. These have lots of fat in them. Try putting sliced avocado on a sandwich instead of the cheese. Its a much healthier fat source!
Thirdly - Focus on fresh fruits and vegetables. No one gets fat eating salad (unless its topped with meats, tons of dressing and cheeses), so have lots of fresh stuff for her to eat along with the rest of her meal. You don't have to limit the quantity of what you eat if its healthy, so limit the meats and refined carbohydrates, and give lots of vegetables.
Lastly get her moving! Limit TV/video game/book reading time to about 30 min a day. Have her run around and play, a ball to kick in the back yard can provide lots of fun - especially if you play with her.
Best wishes. You're not alone, and you can do this!