Realistically, no. The air conditioner will take about 130A when running on its own, assuming the specifications are correct. The Jeep has (according to the specifications for the current model year) either a 160A or a 180A alternator. That leaves either 20A or 40A for everything else, assuming it's running full-out all the time; and at idle or low engine speeds, it can't put out full output, nor would it be happy doing so long-term--it would likely overheat and die pretty quickly.
Even if it did, getting that much current efficiently to the trailer would be impossible via the standard seven pin connector. You'd have to run a separate, quite heavy charge/inverter power line. More effective and efficient would be to have the inverter in the Jeep and run a 120V line.
