This is without a doubt the best post I have seen on this forum in a long time, but unfortunately, you're going to find you're out of luck.
Section 5 of the Marriage Act 1961 defines marriage as: "the union of a man and a woman to the exclusion of all others, voluntarily entered into for life." There's no definition for 'man' and 'woman', so interpretation reverts to the ordinary meaning, and unfortunately, an automobile is by all accounts a vehicle, not a homo sapien of the female sex (or a 'woman').
Conclusion: In Australia, you can't have a legally binding marriage to your car.