I've done this twice in the past few years, most recently in July towing boat/trailer from PA back to NJ. I feel your pain and for something that happens all the time, you'd think the DMV/MVCs would specifically address the trailer issue more clearly... but I think they consider a trailer a vehicle so when they provided the explanations about driving your vehicle back, they also mean trailers. There are basically two answers to the question: the technically correct one, and the practical one.
Technically, I believe, in both NY and NJ you need to have your trailer registered regardless of when you bought it. Which gives you three options:
1) get the notarized bill of sale and other materials you may need to register in NY and go to your DMV to get some plates before you pick up
2) if the dealer is set up for it, they can issue a temporary tag
3) per NY DMV and NJ MVC , you have to get a temporary tag from NJ (
New York DMV | How to get in-transit vehicle permits (temporary registrations) (ny.gov)) "If you purchase a vehicle in another state, you will need to go through that state's DMV office to get a temporary plate and registration to transport the vehicle to New York." . Here is the link to the NJ MVC site on how to get a non-resident temp tag
NJ MVC | Temporary Non-Resident Registration (state.nj.us)
Practically........Given the headaches and back-ups that persist at the NJMVC, I would (and did) just tow the boat home with no plate and throw myself on the mercy of any officer that stopped me. Given the backups at MVC and the fact that you just bought it, I'd have to believe that an officer would probably just give you warning. I didn't get stopped, but even if I did, from what I was able to find out; driving without a plate is like a $50 fine. Which leads me to what not to do...... lots of folks will tell you to use a plate from another trailer that you or someone else has. This may help keep you from getting stopped, but if you get stopped for another reason and they find out the plates are not for that trailer, then you are driving with false plates which is an order of magnitude worse (as now you have shown intent to deceive)
As I mentioned above, I hadn't been able to find anything definitive in this topic, and this is only my best interpretation of what I've been able to find online. So take the above with a big grain of salt. Hope it helps, nonetheless.
