That's actually a pretty basic workup. The only test that's being done at the right time is the progesterone. Normally doctor's check it at CD21 to check for confirmation of ovulation which *supposedly* occurs on CD14. An elevated p4 (progesterone) could signal ovulation.
The FSH should ideally be done on CD3, along with Estrogen (E2) and I think LH if I'm not mistaken. I had a workup of about 32 blood tests for infertility. You definitely need your AMH tested as well as total testosterone, free testosterone, prolactin, and check Vitamin D. I would go back to the doctor and ask for these tests to be done on day 3. That will give you a complete picture of your hormones for infertility and give you a great place to start.
FSH (follicle stimulating hormone) and AMH (Anti-mullerian hormone) are related to egg count and quality.
Hope this helps!