You can check your luggage through. Just show them your Qatar reservation when you check in in Cleveland. most airlines have interline agreements (a notable exception is Southwest; definitely AA, Delta and United do.)

The international terminal is accessed by a rail system. Depending on what terminal and gate you arrive into it can take 15 plus minutes or so to walk to the connecting point, which is outside security and beyond the check in counters.

It doesn’t take very long to go between terminals, but you will have to go through security in the international terminal. You can do it all faster but I’d allow 2 hours between flights.