Microwave and a 15 AMP Breaker

From time to time when starting my microwave the breaker shuts off in the main panel. It doesn't trip the breaker every time of use. Only the microwave itself shuts off and has a plug directly behind were it goes. I replace the breaker on the panel with a 20 AMP and all is good or does the wire from the breaker also need to be changed out. Is this a job for a certified electrician or a simple do it yourself. If only the microwave is causing the breaking to go from time to time is it safe to say this is a direct dedicated circuit for the microwave and nothing else is on it. Not sure if you can buy a microwave that will run fine on a 15 amp breaker, maybe one that has a lower output power. Thanks for any info.

General Info:

Microwave output power is 1100w
Breaker shows 120/240V 10 KA- 15 on the handle (15 AMP)
Stamp on inside of panel door is 982951 (1998 is the age of panel ?)

Microwave and a 15 AMP Breaker