I recommend that you first consult your owners manual. My 2014 Subaru Outback is rated for 1000 lbs without brakes and 2700 lbs with brakes. That is a significant difference. Both limit the tongue weight
to 200 lb.
Too often tow ratings are considered to be how much the vehicle can pull. Just as important, maybe more so, is it's ability to stop with the load.
When I ran a parts store, young guys would come in all the time to get performance parts to, 'make it go faster'. When they came to buy brakes for it, it was, 'give me the cheap ones'. Do tell??!!!
You would also do well to check Trailer Weights in the Real World here, to get an idea of what that trailer will weigh, if you haven't already weighed it. These are actual weights of trailers loaded to travel:
You can sort this Excel file by brand and length.
Glenn's point is well taken. Cheaper to replace trailer brakes than TV brakes.