To give you a response that is more specific to you, I might ask for additional information. Do you have status, the AAdvantage card(s), or have you purchased MCE in advance?
In general, it completely depends on the gate agent, aircraft, and local baggage measuring "culture". I've had gate agents measure my bag as a first class passenger (that REALLY ticked me off), and other agents not even bother with ANY passengers...that element is hard to predict. I have traveled with the same sized overhead-compliant carry on for years, and can offer you this advice. If you are boarding in anything later than group 5, you run the risk of having the gate agents require you to gate check the bag, due to space filling up in the overhead bins. Group 6 on a full flight is when they generally get the news from the crew that space has run out.
I have no way to guess whether your carry-on will be sized by the agent...your described dimensions seem compliant. That entirely depends on the mood and need to assert their authority personality of the gate agent. I will say that some flights over others tend to have more passengers attempting to "push" the carry on limitations, but to my experience CLT-FCO is not one of them. Again, it all just depends on the GA that day. As I said above, I think the biggest factor you face is when you intend to board and what boarding group you will be assigned. If you are unsure of that, you might check the thread for AA boarding groups/procedure.
Best of luck!
Leighjohnwi