I don’t know the specs on the ZZR, but my rule of thumb is that if you shift before you’re halfway to redline, you aren’t really getting much range out of each gear. I think your 600 redlines at 14,500 rpm, so you could easily take it to 10-12k before shifting.
It will take some getting used to because the engine will be screaming, but it’s a normal novice mistake to not be using the higher end of the power range. Some folks hate that upper range, but those folks do not typically stick with the sport bike class for very long.
I would bet that you should be able to hit 35-40 mph in 2nd gear. It shouldn’t be where you cruise, but you should be accelerating in that range.
If it’s not accelerating when you turn the throttle and you’re hand is off the clutch, you have a mechanical problem.