I've been playing off and on for about a week now, and yeah, you can only make a federation character at first, then when you reach lvl 6 the Klingon faction opens up to you. From what I have read the Klingons quests involve mostly pvp and some pve stuff, but is nowhere near the storyline that the federation has. Also, Cryptic is going to be putting more focus on fleshing out the Klingons in the first major patch, and more factions will be released as the game goes on. Like Cardassians and Orions (I think).
Thats about all I know at the moment. I was really looking forward to making a Klingon at install, and it was a suprise to me to find out that you have to unlock it.