Doctoring rhymes with:
factoring, hectoring, administering, altering, bantering, bartering, battering, bettering, blistering, blustering, bolstering, buttering, catering, centering, chartering, chattering, clattering, clustering, cluttering, countering, encountering, entering, factoring, faltering, festering, filibustering, filtering, flattering, flustering, fluttering, fostering, frittering, glittering, guttering, hectoring, kettering, lettering, littering, loitering, mastering, mentoring, metering, mitering, monitoring, motoring, mustering, muttering, nattering, neutering, pestering, petering, plastering, puttering, reentering, registering, scattering, sculpturing, sequestering, shattering, sheltering, shuttering, slaughtering, smattering, spattering, splintering, sputtering, stuttering, sweltering, teetering, tottering, tutoring, unflattering, uttering, watering, wotring
Doctoring sounds like:
destroying, doctrine's, doctrines