Is the transmission really has a slight delay and unresponsiveness?
Since this vehicle is at most two months old the question is, did it do this during the test drive? What did the salesperson say about it? What does the service department say?
Does it have the auto-stop, that might be what you are experiencing, try disabling the auto-stop.
take it to the dealer is the only answer you need on a brand new car . Most transmissions are electronic now and it may be as simple as a ECM upgrade . And I agree if it has stop/start (the most useless feature they have come up with yet) that might be what you are feeling like the previous poster said because if you are sitting and the engine shuts off completely it is going to take a second or two before its going to move. I wont buy a car that you cannot at least shut it off . I still think it’s a dangerous feature .
Try a test drive in another Cherokee on the dealer lot. If it does the same thing, that’s just the way it works I expect. As mentioned above, at some point there may be a software update to address this for the transmission shifting algorithm. May take some time. They can’t change the software willy nilly b/c it could affect the emissions rating.