Have you tripped a breaker yet?
A 15 Amp breaker is good for 1800 Watts.
Though if the Code is considered, it only allows a circuit to be loaded 80 % of its rated load.
So a 15 amp circuit can carry only a total of 1440 watts, which is 80% of the 1800 watts.
Does the outlet or power cord get warm?
If a breaker hasn't tripped and the outlet or cord isn't warm, and you don't have Federal Pacific breakers, I think you're ok.
Keep in mind, it's not really a constant load.