I'd suggest CEVA. Cost me $650 to bring my zed from Vic to QLD. Not sure if this was a special rate though. I know many people that have used CEVA without any dramas.
I recall the seller having to jack my car up to get it on the truck safely. I am sure they can accommodate for a low car though.
I just called them and they gave me the same quote and a quote for the car to be fully covered quote of 845
driveable or not? Will make a huge difference. Cost me $500 to move a '95 300zx from Sydney to Brisbane, using Door to Door Car carriers http://www.doortodoorcars.com.au/contact.htm An non-driveable fairlady convertible rolling chassis was $1200
I used CEVA from Bris to Melbourne, 95mm clearance and no lip damage. very happy with them, was about $700 ish which was cheap too at the time.
Car starts and drives but is not registered and I dont think the current owner will remove the bumper for me ceva sounds like the way to go
I too used CEVA to transport my slicktop from WA to TAS. If the car is on stock suspension it should be fine. Lowest point needs to be minimum 100mm from memory, but they do have special trucks to accommodate lower vehicles but cost more.
I have used these guys a few times ex Qld (MT Andrews) .. always a reasonable price as they do a lot of Trade Cars : http://macleaycbd.com.au/andrews.html