you can certainly tow a trailer that far but you dont mention what trailer
they have everything from 100# to 100000# trailers.
Hard to help without you providing basic info needed.
most of the bigger uhaul trailers pull badly with high drag
and are build heavy.
I'd consider an open style utility trailer and tarping for weight savings.
or perhaps rent a truck and tow your car on a car hauler.
you might also consider buying a trailer, then selling it when you get there. It could end up being cheaper than uhaul.
the major problem you will have is subaru's 1000lb unbraked requirement.
and all the trailers with brakes are imo too heavy with any load in them.
you also dont list what kind of towing setup you have on your car.
anything with surge brakes only requires a 4pin
electronic brakes would require a brake controller and 7pin
edit: after some research
uhaul has a 5x10 enclosed with surge brakes that weighs 1250#
that is probably the best. However that leaves you aprox 1000# capacity
they have a 5x8 thats 300# lighter which would be better but.. with no brakes thats not good.
and finally they have a 6x12 but at 1920 empty weight its too heavy.
how much stuff do you have to move(more basic info needed)