I felt her saying "your first command" was the writers way of telling us this was Kirk's first command without having to spell it out.
And now you know it wasn't.
The Making of Star Trek may say so, but that doesn't make it canon, does it?
"Canon" is beside the point. TMoST, as I said, was written during the production of TOS by an author who was immersed in that production, directly interviewed its creators, and had access to its production memos. It reflects the plans and intentions of the show's creators better than any other source. I'm always surprised when I encounter people who haven't read it, because it should be essential reading for anyone who's more than casually interested in
Star Trek.
TOS was, after all, made mostly by WWII veterans, people who had some insight into how the military works. And they would've therefore been aware that commanders need to work their way up from smaller ships before they're given command of the biggest capital ships.
And...since when does starfleet have anything called a destroyer?
The actual line in TMoST -- which, I cannot stress enough, is immensely worth reading -- is, "Kirk rose very rapidly through the ranks and received his first command (the equivalent of a destroyer-class spaceship) while still quite young." So no, not an actual destroyer, but an analogous category of vessel, a smaller craft with a smaller crew. Perhaps something analogous to the
Oberth-class science vessels of the movie era.
Several works of tie-in fiction have referenced Kirk having prior commands before the
Enterprise. DC Comics's first annual showed him being transferred to the
Enterprise from the
Saladin, which was named for a destroyer-class vessel in Franz Joseph Schnaubelt's
Star Fleet Technical Manual, though it was drawn to look like a
Baton Rouge-class ship from the
Star Trek Spaceflight Chronology. Not long thereafter, the novel
Enterprise: The First Adventure by Vonda N. McIntyre -- which clearly drew on TMoST for some of its specifics -- showed Kirk in command of the
Lydia Sutherland, described as a "little cruiser" with about half the
Enterprise's crew complement. And the "Star-Crossed" storyline by Howard Weinstein in DC's second TOS series showed Kirk's first command as the
Miranda-class
USS Oxford. I don't think there's ever been a tie-in claiming that the
Enterprise was Kirk's first command -- probably because all the authors read TMoST. This has always been the default assumption.
I don't recall any canon reason to think he had a pre-enterprise command, though, if you discount Dehner's line as open to interpretation either way.
And I don't see any reason to default to the assumption that he didn't, because that's the less likely interpretation by far. As a rule, nobody would be given a ship of that class until they'd gained some command experience. It would take extraordinary circumstances, like those in the 2009 movie, for an exception to be made. And even that exception strains credibility to the limit.