That comment you mention about "minor member of the Resistance" is actually in an intelligence file that Kira reads in the episode "Battle Lines." Possibly written by Dukat, but certainly not spoken aloud by him. Kira is not happy to hear about it, so she obviously thought of herself as more than just a "minor" member. Maybe others did too.
Besides which, I think the idea of Dukat writing that is kind of inconsistent with the idea that her mother was his lover for a while. He knew very well who she was all along. The novels suggest that he deliberately downplayed her importance in official files to protect her on Meru's behalf. Which would also suggest that she was indeed more important than "minor member" would imply.
It's probably the same situation as Starfleet faced during and after the war. So many officers had been killed in battle, people were getting promoted and given command before their time. We know there were older officers around - General Krim and Colonel Lenaris for example - but they had higher ranks. Maybe in their minds a comparatively minor role as "liaison officer" - basically a make-work job - didn't need anyone older than 26.
Don't forget also that Kira suggested she had been assigned to DS9 almost as a punishment from her superiors. They wanted her out of the way because she was a loud-mouthed complainer, and the furthest they could send her was off planet. If that role required her being given the rank of Major (which was basically honorary anyway, until this point there had been no Militia for her to earn such a rank in), then so be it.