What reason do we have to think that Leonard McCoy was a doctor when he killed his father? He could have done that in the role of next-of-kin instead. And he could have been of any age, from six to forty-six, since his physical looks in the Sybok-induced fantasy would not really reflect his true age. All we know is that he "looked for the cure" - but a layman (or a laychild) can do that just as well as a doctor might.
We have very little idea about McCoy's early history anyway. There is no indication yet that he studied medicine first and joined Starfleet thereafter, even though many novels assume this. Nor is there evidence against him earning his PhD and officer commission within the standard four Academy years - after all, other, later and better-known bios suggest that engineers can get their demanding academic-level training within those parameters easily enough.
All we really know about McCoy's story is his birthdate (thanks to "Encounter at Farpoint"), the number of years he served as starship CMO (thanks to ST6:TUC), and a couple of rather fuzzy glimpses to his career aboard the Enterprise (with no indication that we would be seeing his first year aboard, or his last year, or anything). Those, and a very fuzzy reference in "Trials and Tribble-ations" for him having been at Ol' Miss (which may or may refer to a certain real university) for some indeterminate reason (student, teacher, school nurse, visitor, beau, burglar) during one of the lifetimes of Dax (and we have no real idea about the specifics of that lifetime). Basically, everything is open to wild speculation here.
Thankfully, Memory Alpha appropriately marks the speculation there as such.
Timo Saloniemi