My response is from a few different points of view - one as a mother and the other as someone who's worked in the field of Diabetes for over 8 years.
Though not impossible, it's quite uncommon for children to develop Type 1 diabetes as infants. But, no one really understands the spontaneous auto-immune disorder that prevents the beta cells from producing insulin in these patients.
The traditional signs of Diabetes are polyuria (excessive urination), polydipsia (excessive thirst) and polyphagia (excessive hunger).
Because the insulin isn't delivering the glucose to the cells, it is excreted in the urine which will begin to develop a sweet smell. This is usually when it's quite extreme. Also, as the cells are deprived of energy (glucose), someone with type 1 diabetes will have a really hard time keeping weight on them.
Type 2 diabetes is completely different, and it's usually associated with obesity as the body begins to produce less insulin and becomes resistant to it. It's on the rise with kids in the US, but this doesn't sound like anything you're experiencing.
So, as a Mom - I think everything is completely normal - she's just getting to a different phase in her development making her more clingy, more interested in foods and having different metabolic needs than she did a few weeks ago.
I don't see ANY reason that ice water is bad for her. A sippy cup/bottle will regulate the amount of water getting into her belly. Juice isn't bad, but I'd personally recommend watering it down simply because I didn't want my kids getting accustomed to the full flavor and the needless calories.
If you're really concerned, call the pediatrician. If you're a first time mom, they're used to these calls and would rather you bring her into them now than wait for ketoacidosis (if she really does have diabetes) and an intensive hospital stay.
Good luck! I honestly believe all is OK.