Trailer it with engine toward tow car and try to get it balanced on the trailer so it has a little weight on the tow bar, otherwise, if the weight is to the rear of the trailer, it will be trying to lift and point the tow car.
I hope the tow car is up to the task and weighs more than the combined weight of the ute and trailer.
That's the law.
Strap it in two spots forward and two spots rear, and preferably outwards to each corner of the trailer, from solid points on the ute so it cannot move.
Use good straps/chains.
Don't worry about the ute suspension moving, that should not bother you.
If for any reason the set up starts to sway, DO NOT TRY TO DRIVE OUT OF THE SWAY, slow down preferably using the trailer brakes, if the trailer has working brakes ???.
If the trailer has no brakes then don't go too fast and leave plenty of stopping room between you and anything in front.
I have never towed a car on trailer without trailer brakes.
If the trailer has brakes learn how they work by using them when going slow, before you take off on the highway.
If they are electric brakes, you may have to adjust the controller more than once to get them right.