If I have a conviction for drink driving and reckless discharge of a firearm, am I able to go to Australia just for a holiday?

Probably not

if you havnt been sentenced to prison for over 12 months, you should be sweet

Its true that sentences for more than 12 months may stop you from entering Australia, BUT the fact you have a firearms conviction will be reviewed irregardless of the time spent in prison.

Firearms, domestic violence, drug trafficking, previous declined entrances, pedophile charges may all be reasons to decline you entrance to Australia due to the nature of the crime committed.