If they have any sense they will do a GAD test to see if you have antibodies associated with type 1, which is an autoimmune disease.
At the same time they will consider:-
- How old are you?
- What's your BMI?
- How did you present when you were diagnosed with diabetes? Did you have high blood sugar (>30) did you have ketones? Had you had dramatic untried for weight loss pre diagnosis?
Reference range for c-peptide is 0.26-1.03 nmol/L, so you are producing plenty of your own insulin.