Hope you got it home without incident.

Tilt bed eqpt. trailer should be good, low bed even better, but they are right in saying you gotta know the tare weight of the truck 1st. A 10K trailer isn't all that light & combined with the weight of the truck may be over 10K.
You do not want a case of the tail wagging the dog with that big a load, get up to a pucker factor 12 at the least. :p

1956 GMC 370 dump " 'Tater "
1970 VW Volksrod "the Black Bomber"
2007 Chevy Avalanche
2020 Jeep Cherokee Trailhawk,
2005 Harley Davidson FLHTCUI

I dig all cars, old and new, whether they were hammered out of American iron, German steel, or Japanese tin cans. Being unable to appreciate them all is missing out on a world of great things.
But thats just MY opinion! :P