The Pennsylvania Driver's Manual states that if you plan on using your learner’s permit for driving outside of PA to check with your insurance company and the other states’ Department of Transportation (or Department of Motor Vehicles) to make sure your learner’s permit is valid.

So it would appear that PennDOT allows for you to drive out of state with a learner's permit but you would need to check with your insurance company to make sure it would cover you driving out of PA with the permit.

You also would need to verify with the New Jersey Motor Vehicle Commission (MVC) to find out for certain if your Pennsylvania learner's permit will allow you to drive on their roadways.

We have read that with a valid learner’s permit from another state one may legally drive in New Jersey provided the vehicle he is operating is properly titled, registered and insured in the home state. They note that the permit holder will be subject to the laws of his or her home state. 

Again we would advise contacting the NJ MVC to make certain you can drive there with your PA permit and to find out exactly what restrictions or conditions you will have to adhere to while in New Jersey if you are permitted to operate a car there.