We have drink drive laws in Australia and the police do hang out on the roads at anytime day or night.
I can assure you that in Cairns they are there 24/7. It isn't worth driving if you are going to drink, even if you think you will only have one beer!!Why spoil at good night/day out for the price of a couple of beers.
Taxi's are readily available here. The waiting time is excellent, they come pretty well straight away, you may have a wait if there is something big on in Cairns, example, if it's a big race meeting.
There are a number of Taxi ranks in the city area.
OR you can ring them, just make sure you have an address to give the operator, stand in front of a restaurant or pub and give that name to the operator, they don't like picking up from random areas, like a phone box!!!!
If you need one from the restaurnat you have been at, they will ring for you.
If you are going to the airport, book a cab ahead. It would be best if you are outside to meet this cab, remember to book a time that will give you plenty of time to travel to the airport and allow you the hour before bookin that is required for domestic, and also whatever time you need for International.

