Wirelessly posted (BlackBerry8530/5.0.0.601 Profile/MIDP-2.1 Configuration/CLDC-1.1 VendorID/417)
The OP is not checking any dogs. He indicates that the dogs are traveling "in cabin."
If the OP is traveling on paid -- as opposed to award -- tickets, Delta's tariffs provide that Delta will provide ground transportation between JFK and LGA for connecting, international tariffs. I would carry a copy of the pertinent part of the Delta tariffs, and let Delta take care of the ground transfer.