I have a rental listing you may want to take a look at it is a 2 bedroom+ available now just dropped the price to 1425.00 per month...I would be happy to ask the home owners if they would consider a small cute dog like a Maltese.
I understand your looking in Jersey City Heights my rental is in West Bergen right down the street from the light rail easy access to everything.
Shops, Restaurants, Park down the street for your dog and the street is lovely as well as the home!
If this sounds of interest to you check out my rental on my site it is listed here on my trulia site or if you prefer I can send you an email just drop me a quick note.
All the best,
Re/Max Villa Realtors
Serving Hudson and Bergen County~
phone mobile is best 201-970-6064