I highly suspect that your TV cannot handle the tongue weight plus people, pets and cargo. If I were you, before you do another thing, I would get an actual tongue weight. Then I would weigh the TV by itself (with driver and full tank of gas) and subtract that from the GVWR on the door jamb sticker. You need to know what your max. TV payload is.
How do you know what the trailer weighs? Did you just weigh the trailer axles at a scale? The gross trailer weight would be the weight on axles plus the actual tongue weight, then 10-15% of that as you say. The unloaded weight is of no use. You want the weight of trailer with all your typical cargo. Factory UVW weights and cargo carrying capacity (CCC) weights are useless for anything.... Same with factory listed dry tongue weight.
You need to figure out the actual tongue weight so you can get the correct spring bar rating. Don't guess on it. Your actual tongue weight *could* be up around 1,200 lbs. If you had say a 1,000 lb rated bar, the tongue weight should not be over 1,000 lbs., so it's important to know your tongue weight for this.
If you drove the trailer home without a WDH, that's scary IMHO, esp. for someone inexperience with towing a TT. If it turns out that your TV is significantly undersized for the trailer, that's also potentially scary.
There are various WDH hitches out there and it depends on what you want. Cheapest price? Integral sway control? Add-on friction sway control? I would not tow without sway control, esp. for a trailer that long.
Providing your TV can handle the trailer, it really helps to take both to the scales and really figure out what all the weights are and what the WDH is doing.