Should a buzzing circuit breaker be replaced for safety?
If you're getting noise, either the breaker is failing or the wiring is getting loose and so can vibrate.  It might be a simple as tightening the connection that holds the wire into the circuit breaker.  If this doesn't fix it then you can try replacing the breaker.

Don't play with your main panel unless you know what you're doing! :)

BTW, the circuit breaker should not trip unless there is too much current going through it. Are you in the USA? If so, your power is 120VAC. The two standard breaker ratings are 15A and 20A, which should handle 1800W and 2400W, respectively.

So unless you have other significant loads on the same circuit I would not expect the breaker to trip.