Just do the Fed PvE missions until you hit Lt 6, they're silly easy and give great XP so you'll level fast. It can be done literally in just a few hours of play.
Then be prepared for grinding a handful of PvE missions and/or PvP to level your Klingon.
Unfortuantly, PvP at low levels is almost non-existant these days.
Also since you did lvls 1-6 your unlocked Klingon will be lvl 6 so you wont lose any time involved. You will need to take a very long shower to get that god awful Fed stinch off of you . Also place a condom over your cpu while your on that side.