The northern route through Russia is certainly doable and reasonably safe. If you want to minimise the amount of kilometres your car is transported by boat, then look at having it shipped from Darwin to somewhere in Indonesia. From there, you can travel via Indonesia, Singapore (there are ferries connecting the islands), then up through Malaysia, Thailand, Laos, China and into Russia.
Once in Russia, you can of course drive all the way into Europe, but you might also like to consider visiting Mongolia and Kazakhstan along the way.
You'll need to invest a lot of time into arranging the necessary permits to bring your vehicle as well as visas for you and your travelling partners. Be prepared for lots of bureaucracy. There are commercial agencies which specialise in arranging visas and vehicle permits.
You other option is the southern route. It's very difficult getting vehicle permits for Myanmar, so your best bet here is to have the car shipped directly to India. From there you can tour around India then drive through Pakistan, Iran and into Turkey, Bulgaria and onwards as you please. Again, be prepared for lots of bureaucracy getting all your visas and permits, and be aware that the security situation in Pakistan is unstable (you may want to rush it, and stay as far as possible from the Afghani border).