What level do you have to be to start your own crew or your own faction? I can never remember this...
According to this site, it's after you do your 3rd "Meet with..." critical mission, after having at least 16 reputation and a minimum level of 10. Not sure on the accuracy of those numbers, but that seems to be in the ballpark. I remember getting the "Meet with..." mission unlocked my 'captain' status around that time on other characters.