Wizardfromoz: It is a relatively straight forward process, although there is no assurance the visa will be issued. You/She need to supply the application document. (Go to the Aus embassy website in Moscow and go to the visa section. All the forms/info are available in both Russian and English.)
She needs to supply a reasonable assurance she will return to Russia, IE: Children are a great benefit under these circumstances, leave documents from a registered university or place of work is another good one, real estate and or other tangible things which will be of loss to her if she did not return.
You need to supply at least but not limited to, a letter of assurance that you will underwrite all financial costs and ensure she doesn't overstay her visa, a rates notice from your home or similar, pay slip or group certificate, telephone and electricity account to demonstrate you do actually live where you say you do and a copy of your passport is helpful. A bank statement from at least one account to show you have some money to back up what you are saying.
This is not difficult to put together and it is a good practice run for the later process anyway. From date application is lodged in Moscow, from my experience (Having done this several times for my now wife and also my MIL) it usually takes less than two weeks to process.
The trick is to write your letter and sign it, then scann it in high quality along with all other documents and email to your girlfriend. She completes her documents and then she can send the lot express to Moscow. You should be able to wrap the whole thing up in 1-3 weeks if you don't try to short cut.
I understand that prior to my pulling this one quite some time back, it was very rare if not unprecedented. I now know of several people who have invited their fiance'/girlfriend here on visitor visas.
If you are stupid enough to do what we did and fall in love somewhere during this/these visits, there is a big disadvantage and that is you create for yourself a living hell when you put her on the plane to go home, with the only hope of seeing her here again for a while depending on the visa clerks in Moscow approving your application for an SC-309 which can take quite some time. (Up to 10 months with no assurance of approval) Get it into your head right now that it is hell and nothing more. The very thing that is designed to bring you together in the long term has the potential to be the thing which breaks you apart. God knows, my Mrs and I can vouch for that.
All of our applications and the entire process has worked without a hitch, but very very slowly.
I/O