There was a big discussion on her on one of the bbc comms a while back. Of course I can't find it now though, sorry. But since she didn't go to the crime scene the consensus was she wasn't probably a doctor of any sort.

http://www.bbc.co.uk/programmes/b018ttws/characters/molly-hooper says she's just a lab tech though

When I was writing my fic where John became a medical examiner this helped me, it might help you figure out Molly's position: http://www.met.police.uk/scd/specialist_units/forensic_services.htm