If OP gets a dolly that pivots, then he needs his STEERING wheel locked. Either by its own locking device, or by strapping it. If he gets a dolly like the ACME, then he needs his steering wheel unlocked.
If his new car does not lock the wheel, I'd recommend the ACME so he doesn't have to mess with strapping the steering wheel. I've used our ACME with both kinds of steering, and it's very easy to leave a locking steering unlocked.
More and more cars do not have steering wheel locks. That points to bigger future market share for dollies of the ACME style than the older pivoting style.