Your daughter's results would get her diagnosed with diabetes. My daughter's endocrinologist told us that any reading over 180 will get a diagnosis for a child. Your daughter has frequent high numbers. Her a1c of 6.0 means an average blood sugar of about 130.
Type 1 or type 2. Firstly type 1 can be antibody negative. The doctor should do some more tests looking at c-peptide levels, insulin levels, etc. to see if this is deficiency of insulin or high insulin / insulin resistance.
Being overweight is neither here nor there for a diagnosis. But beware, some doctors may immediately assumed type 2 based on her weight. Type determination should be based on other factors as mentioned above.
I suggest that you start monitoring how much carbs she is eating. Carb restriction is definitely on the cards. This means more than just restricting candy, but also managing other sources of carbs such as grains, fruits, starches etc. If it is determined that she has insulin resistance then an oral medication such as metformin may be started, and when combined with exercise and lower carb eating, can be very effective.
If type 1 is determined, then treatment is insulin along with carb management.
Control of blood sugar levels is going to be critical for health.
I would suggest the following book:- Diabetes Solutions by Dr. Richard Bernstein. Whether you decide to go as low carb as he recommends or something a bit more moderate, there is heaps of useful information. "Bernstein Diabetes University" on U-tube may also be of interest, and there are more than 200 information sessions.
Typeonegrit facebook page is a very supportive community of parents of kids with type 1 and people with type 1. I enjoy the support and information I get there, specifically for kids.
This tudiabetes community is also an incredible and supportive community. The generosity of people in sharing time and experience is priceless. So keep asking anything at all.
To assist your whole family and support your daughter, you might want to consider moderating the way all of you eat.... to reduce carbs. Low carb seems to be all the rage these days (perhaps with good reason), and there are increasing great resources. Key words include: paleo, ketogenic, low carb, primal. I love the recipes at http://alldayidreamaboutfood.com/ and http://mariamindbodyhealth.com/
Hope this response is useful for you.