I know at least 3 people in Australia that have (spent) drink driving convictions. One works for Virgin Blue, one works for Qantas and the other used to work for Ansett.
Whether or not they put any thing down on their forms is another thing. As far as I can tell, one conviction isn't a problem but more will be viewed with suspicion.
For the medical, you can be honest, if you regularly get done for DUI then they might do a liver function test. In fact, they still might for one only. As for the airlines, you don't have to tell them per se, you can put down "traffic violations" or something.