We don't have a Triple Crown as such, not on the same scale as yours.
The major cities of Australia ( Brisbane, Sydney, Melbourne, Adelaide and Perth ) all have their own 3 year old classics, with Sydney and Melbourne being the main focus of metropolitan racing over here.
The main 3 yr old classic in Melbourne is the Victoria Derby which is always run in November, on the Saturday before the Melbourne Cup. there are a number of lead up races for the Derby but no real 'Triple Crown'.
In Sydney the big carnival is run in April and there is a three race series for 3 year olds which is referred to as a 'Triple Crown'. The three races are the Canterbury Guineas (1900m) the Rosehill Guineas (2000m) and the AJC Derby (2400m) but there isn't a great deal of promotion or much emphasis put on about the series.
So to really answer your question, do we have a Triple Crown Series here that is as important to us as your Triple Crown is to you....No we don't.