Why do you want a trailer just wide enough or strong enough for the TC? The TC weighs about 5400 lbs. I don't know if that includes a bucket. A 7K trailer will be boarderline enough for capacity. TC would probably fit on a 12' trailer (with a little overhang) but you will want more length. Personally, I would look for a 10K trailer in at least 18' length. If you plan to haul the TC and mower, you will want at least 20' length. The 90" mower attached to the TC will not fit between the fender wells of a trailer and the mower will have to sit in front or behind the fenders. The extra length will help you balance the load better. The wheels on the 90" mower will just fit on the deck of a full width trailer with fenders. You will want a trailer with 82-84" between the fenders. The cost of a longer trailer does not add much to the price of a trailer.
If you want to haul the mower, TC and another attachment, you will need a 24' trailer. I hauled my TC home with 90" mower, bucket, PHD and 12" bit and it took most of my 24' 14K trailer. PHD was partially in the bucket.
By the way, congrats on you purchase!
If you don't plan on hauling the TC much, consider renting a trailer.