The generator should easily handle a 13,500 BTU A/C, even a 15,000 BTU unit. You'll have to make sure your converter/charger isn't pulling full amps to charge batteries, and a soft start capacitor would really reduce start-up amp draw for the A/C, especially if you have the larger 15,000 BTU unit in mind to power. You'll also want to check your refrigerator heating element or turn fridge to LP gas only.
Bob & Donna
'98 Gulf Stream Sun Voyager DP being pushed by a '00 Beetle TDI