I believe CIL do. www.cilinsurance.com.au/ They are definitely my choice for no hassle claims.

G'day The Stig,
Welcome to the forum - I trust you will get as much out of it as I & many other members have.

I had no issues with RACQ but that's only for a part-time use. CIL does have a good reputation.

I used to use CIL but had a bad experience with them when I submitted a claim, so now will not use them. I am now with QBE but found getting a claim approved somewhat time consuming. I am planning to go with RACQ but have not yet checked out their conditions re full time life in the caravan. I was talking to someone from RACQ recently and they told me that NRMA is now owned by RACQ too.

Not totally relevant to caravan cover but when my daughter recently had to have some panel beating done I asked the owner there which insurance company was the best for allowing a good job to be done and not screwing every last penny out he answered that Shannons and QBE were both line ball and very good to deal with.

Shannons clearly not suitable for grey nomads but no reason to think QBE would be any different cars vs caravan repairs.
Of course, this panel beater would have no experience with CIL.

Just some added info for what its worth.

BTW...daughter was insured by RACV. No hassles. Good job done.

Jim