Stock Saddles (The true name for an 'Aussie' saddle) were made for cattle work. They were made for stockmen and drovers who spent the whole day moving and droving cattle.
A stock saddle can fit any horse - It just depends on the individual saddle. Most are made on a standard 'stock horse' tree (I.e. Australian Stock Horse, not QH) but there are many that are made specifically for different shaped horse. Nowadays you can even get some half breed fender saddles made with QH bars.
In case you don't know - There are two types of stock saddle. The traditional stock saddle which has a full skirt and stirrup leathers, and the half breed or fender saddle, which has leather fenders similar to a western saddle but still has the knee rolls and no horn.
The problem with stock saddles in the US is most of them are crap. Badly made and some have a horn tacked on to make them seem more familiar to western riders.
A true stock saddle does NOT have a horn.
To buy a good quality stock saddles in the US you are looking at upwards of $1,000 - And these are the very bottom end of the quality saddles. In Australia, for a quality stock saddle made by a saddler, not a production line, you are looking at upwards of $3,000 - Second hand. They go from $4,000 to $8,000 brand new.
There is a website (James Saddlery? Maybe?) that sells decent quality half breed saddles with more of a 'western' feel to the US - I wouldn't call them true stock saddles but they are fairly good quality and readily available. I beleive that also custom make the saddle for your horse based on wither tracings. There are a few people on here that have bought saddles from them.
Let me know if you have any other questions :]