Flying TLL-WAW on a CRJ900 connecting (with only 1 hour layover) to a WAW-LAX flight. I'll have a full-sized carry on (and a tiny backpack).

Will they have to gate check my carry-on? (If so, am I correct assuming I'll be able to pick it up at the stairs when I get off the plane at WAW.)

I generally have breakables in my carry-on (I bring back Starbucks mugs from every city I visit for my friend, an avid collector.)

On an unrelated note, I'm slightly sweating the 60 minute connection - I'll have to walk to the terminal, clear exit passport control, and I assume by the time I reach the gate my flight to LAX will already be boarding. I have no status, and flying in economy on an award ticket.

Thank you in advance for your opinions and expertise!