Patrick replied:

Sharon,
I assume you are taking the direct route using the Great Central Road from Laverton to Ayers Rock. If so, I did a trip across there a few years ago towing a Jayco Eagle Off Roader. There should be no problem with your Vicount apart from dust. This road seems to be fairly well maintained and a speed in excess of 80kph was possible in most cases. You may still need to get permits from the relevant Aboriginal authorities to travel through this area.
At the time you are planning to travel, there is a National Four Wheel Drive Gathering just North of Alice so there will possibly be a bit of traffic on this road. I am aiming to be one of them.
Cheers
Patrick

Simon replied:

We travelled from Perth to Yulara in June 1999 and took the Great Central Road from Laverton. We purchased the HEMA Great Desert Tracks of Australia Map Pack and found them extremely useful.

Remember, you need to obtain permits to travel through this area.

The gravel road should be suitable for the types of vehicles you intend taking. We saw a Falcon sedan doing the trip!