Well I would step back and review your plans.
Do you plan to rent your home in NJ? Or just leave it empty. Each has issues. The stories or renting are all over this board.
Renting in NH with any dog can be a challenge. If you find anyone that will do this then take it quickly. Most landlords do not accept pets.
Here is the attorneys view of one case.
LINK
The landlords side of the story as read in newspapers at the time was that it was written in the rental agreement "No Pets". The landlords mistake was not initiating eviction notices immediately upon finding out that there was a dog in one of his rental units.
So most landlords do not take pets with rentals. Some do. But liability can be an issue.
And as a delivery person I have heard repeatedly that "my dog is different" and "my dog does not bite" etc. Well, I stopped counting the dog bites at one dozen and that was early in my career.
Good Luck.