What's the noun for doctoral? Here's the word you're looking for.
doctor
A physician; a member of the medical profession; one who is trained and licensed to heal the sick. The final examination and qualification may award a doctor degree in which case the post-nominal letters are D.O., DPM, M.D., DMD, DDS, DPT, DC, Pharm.D., in the US or MBBS in the UK.
“Bayle was not aware that Locke had been denied in 1666 his doctorship by the hostile Oxford authorities.”
“If he was neither the one nor the other, indeed, his doctorship would no doubt avail him the less.”
“Not one came, moreover, without her little pipkin of pennyroyal, sage, balm, or other herb tea, delighted at an opportunity of signalizing her kindness and her doctorship.”
doctordom
The realm or sphere of doctors; doctors, collectively.
“One of the annexes, as I have said, has had thoughts of becoming a doctress.”
“Tell me, when thou wast little, didst thou know Gagaoola the witch doctress?”
“Among her topics are female travel writers and colonial knowledge, fashioning and marketing the doctress of empire, and female medical education in India.”