The coop is 6x6 or the run is 6x6? Or both together? 6x6 as a coop should work great for 6 birds, but you'll need to add about 60 sq ft minimum in run space, unless you're planning on free ranging most of the time.
Rough minimum is 4 sq ft per bird in the coop, 10 sq ft in the run. You can fudge it a little but overcrowding can lead to all sorts of issues.
I don't have any experience with electric but another possible option is to get a chain link dog run. 10x10 is a standard size which would be fine for your flock. You'll need to reinforce it with hardware cloth and an apron but that's not very expensive to add on and it's something you can do on weekends.