Then why didn't she say "the Enterprise?" "Your first command" is a strangely distancing way of referring to the ship she and her listener are aboard at the moment she says it. As zarkon says, a destroyer-class ship could be captained by someone of commander's rank. And The Making of Star Trek says explicitly that Kirk did have an earlier command, and that predates StarTrek.com by decades. It was written during the production of the original series by a journalist who had extensive access to the production staff and documents. It probably reflects the creators' original intentions better than any later source.