Can I add a 125amp panel to a current 125amp main panel?
I'm pretty sure you are OK with having a 125 amp sub-panel, even off of a 125 main panel. You don't have to supply the sub-panel at 125 amps, just what you anticipate the load will be there. I have a 200 amp sub-panel in my shop, fed at 125 amps.  You'll of course need the correct size wires and breaker for whatever amperage you choose.  You'll naturally need to treat it as a sub-panel (isolate ground from neutral and provide 4 wire service to the sub).   The Square D QO panels are high quality (IMHO) and shouldn't need replacement like Federal or Zinsco panels.   You may need to free up some space in your main panel to make room for the breaker to the sub-panel by re-routing a couple of circuits. Not sure if your main panel is full or not.   Maybe I've missed something, if so, I'm sure one of the 3 wise men will weigh in!