I've shipped our possessions to New Zealand and back, but not a car. From that experience I'd say it would be cheaper doing it through someone there and paying Aus$ than paying someone £ here. Join an emigration forum and find out who they'd recommend.
It's charged by m3, you will have to share a container unless you want to pay lots and then you will have to wait until there's something suitable to share with. My bike was 2 months later coming back than the rest of our stuff
Obviously with a car there's a lot of air inside that your paying to ship. Might be worth seeing if there's some goods you could invest in to sell here by stuffing the inside
Perhaps diff lockers or snorkels for 4x4's that are like hens teeth here?
Good luck, you must really love it.