My 11 year old daughter has been diagnosed with hashimoto disease, with 2 solid nodules each side(13mm), should we do the biopsy to check for cancer?

Probably: 1.3 cm is big enough to biopsy depending on the appearance of the nodules. At the very least, she will need to have these nodules followed yearly to make sure there is no changes in the size of the nodules.

Do biopsy.: Although cancer would not be expected here, especially since the patient is young, this is an autoimmune disease, and it is associated with other such diseases, like rheumatoid arthritis, systemic lupus erythematosis (sle), and others, as well as associated thyroid issues, like hyperthyroidism. A biopsy can be of great help in finding out if this is the case.