I've travelled with a 2 year old, and I've stayed at a family friendly hostel in Jamaica, but I would never do the 2 together. Public transportation in Jamaica is insane (though riding on an actual bus there was pretty normal). Their inexpensive taxis involve stuffing 10 people into a small sedan, I kid you not. Where are you going to fit a car seat in that debacle? Or, you can pay through the nose for a private car. My experience was 10 years ago, so things may have changed, but I doubt it.
The hostel that I stayed at in Treasure Beach wasn't bad, but it was set on a giant hill. I would be constantly on edge watching my 2 year old so he wouldn't hurt himself. Older kids would have been fine. Kingston had a lot of stray dogs running around. It didn't bother me too much, until I saw some packs when we were out walking one night. Personally, I am all about protecting my kids when they are that small.
I guess my advice would be to really look into all the details before bringing a toddler. Where are you flying into? How are you getting to the hostel? Etc.
ETA: think about sleeping arrangements. Is your kid going to freak out being in a strange place? Are you going to be staying and sleeping in a single room/bed? What time does the little tike go to bed, and are you going to want to go to bed that early as well? (Mine go to bed at 8, and hell no, but on vacation together, one of us has to stay in with them.). My older son was a great traveller until he turned 2 and refused to sleep in the pack-n-play. We ended up having him sleep between us, so he wouldn't fall out, but he thought that was awfully fun and didn't want to settle down and go to sleep. This was on a cross-country road trip.