Tabby, from what I know as long as your remaining teeth are healthy and the missing ones are not visible when smiling, it should be okay. Someone posted the medical form on here, do a search and you can read what it says about the teeth.
NixNix, I would be careful about the visa. Perhaps best to check direct with the nearest Australian embassy/Consulate to your country. It can depend on the reason and if you were working illegally as well as overstaying.
Australian immigration is quite strict, most people will have a ban on re-entry into the country on any kind of visa if they have overstayed. As soon as you used the passport then it would come up on their screens.... (they can see any fine or problem that you previously had going into/out of Australia if officially recorded- e.g. if you ever got a fine from Quarantine, if you ever got turned back at the border etc)
Since one year has passed it might be there won't be any problem. If I were you I'd call & check before you apply to EK. If you apply and they knock you back because of the visa problem, you might not get another chance. At worst, the Aussie government will tell you there is a ban and you'll have to wait it out until the ban is finished. People who have gotten a temporary ban (1 2 or 3 years usually) are almost always okay to come back once the time has passed.
(I have friends in customs, this is how I know about this stuff, hope it helps)
Department of Immigration & Citizenship