I would not be too concerned about a 6yo not being a able to hold a handstand, as long as he can hit a good handstand position before rolling forward. I've found that spending time holding a handstand against a wall (chest facing wall, hands as close to the wall as possible) has helped my son be able to hold it longer on his own. On non-gym nights I'll challenge him to a contest to see who can hold it against the wall the longest. At first I would always win, but lately he's been able to hold it for longer than I can.
I would think that 6 is the perfect age to start teaching bar skills, but to work on strength you could get a pull-up bar and practice pull-ups and leg lifts.