tow capacity question

Yeah, you have to know the weight of the boat. Also you need to check what class hitch you have. Probably set up to handle the tow rating of 3000lbs...but HD trucks don't always have that. There are plenty of pickups with 12000+ tow capacity and class IV hitches rated for 10K....so check.

Doesn't sound impossible to me, depending. I've towed a 2,000 pound m/l standup TT a lot of miles with a 4-cyl.

In your case, it doesn't really matter what the trailer sticker says- without knowing the weight with the boat it's hard to answer the question. Can you look up the brand/model of the boat and get weight info? Sounds pretty small, though and since we do know that total weight cap of trailer is 3,000 pounds:

Unless as noted the tow vehicle's carrying a lot of payload too, I frankly wouldn't hesitate to tow a BOAT with this combination- not the same struggle at all as a stand up trailer. Wind resistance in the latter case might kill the deal- not such a problem with the boat.

One caveat:
The trailer must have its own brakes in this scenario; don't expect your tug to safely stop it. This not to mention that this requirement is likely also in your Toyota owner's manual for towing any trailer over about a thousand pounds.

Assuming the boat is approaching that 2220# number, the only way you will stay within that Max tow rating number is if you (the driver) are the only weight in the vehicle.
All other passengers and "stuff" have to be subtracted from that 3000# number.
Fully loaded the car will struggle.
I used to pull a 3500# boat trailer and I sure wouldn't have liked to do it with a 4-cylinder!
The other detail you need to look at is whether the trailer has brakes. Many States require them on a 3000# trailer.