I don't see how your proposal can prevent double voting. Voting happens over a period of several days not to mention absentee voting.
Plus, it seems to me the process is not particularly tamper resistant during the ballot tallying phase, when compared with what is possible using cryptographic techniques.
Paper voting works in Australia. You don't even need your ID (edit: and by "don't need", I mean "they aren't allowed to ask for it") - you rock up at a polling station in your electorate, give your name, they mark it off on a sheet. You give verbal confirmation that you haven't already voted. They give you a voting paper, you fill it in at a booth, then drop it in the box on the way out.
(If you're so inclined, you can also just get your name marked off and walk out if you want to donkey vote, which is the equivalent to a protest/blank vote. Or draw penises on the voting paper).
If you don't vote, you get a nice letter in a few months from the Australian Electoral Commission with a fine of about $100 or so for not voting. Voting is also on a Saturday so most have the day off, and there are early polling stations open for a while prior to the day so if you can't make it on the day you can do it then.
There is also online voting. At least in the most recent NSW state election there was. I was overseas during the election and attempted to vote via this method. Unfortunately my hotel's WIFI kept timing out and I gave up in frustration. I returned to Australia and there was a $57 fine waiting for me for failing to vote.
I think our voting system is good but it has flaws. I recall reading an article a few years ago about somebody who showed up to vote (i.e. Got his name marked off) at multiple polling stations on election day just because he could. He received a fine for doing it but all of his votes were counted.
Edit - googled it apparently you can be charged with fraud for multiple voting or for voting under a false name (up to six months prison - so slightly more than a slap on the wrist and a fine).
Hmm I wasn't aware that anywhere in Aus was doing online voting! My only experiences have been either Federal elections or Victoria State Elections, which both follow pretty much the same process.
Yes Australia has quite a good system - we just need to get preferential voting above the line for the upper houses. At the last state election I had to number all the candidates from 1 to 410 if I didn't want to give my vote to the faceless back room political operators.
I should mention that a donkey vote is not a equivalent to a blank vote. A donkey vote is when you number the candidates from 1 to x from top to bottom. You actually give your vote to whoever happens to be at the top.
Qld state election required Id. Each voter was sent a registration slip and they had to provide it at the ballot box.
The loss of the senate ballots and subsequent post-election re-run of the entire state - which had a different outcome - was a massive failure of Australian electoral process.
Plus, it seems to me the process is not particularly tamper resistant during the ballot tallying phase, when compared with what is possible using cryptographic techniques.