The three main objectives of the Reserve Bank Australia are as...

The three main objectives of the Reserve Bank Australia are as quoted from their website:
"the stability of the currency of Australia
the maintenance of full employment in Australia and
the economic prosperity and welfare of the people of Australia".

The first point of having a stable currency seems a bit broad but specifically its refering to the effect on gross domestic product of the australian economy. Essentially making monetary decisions to insure that our currency remains competitive and doesn't have adverse effects on our market particapants. (exporters & importers)

So essentially what im saying is if the federal reserve raise there interest rates or cut them we loosely have to follow suit because there currency effects ours, a lot of world trade is pegged to the us dollar commidites are a great example of this. unfortunately we don't live in the 1800's anymore we are a global economy and when the top economy in the world makes decisions they have large reaching effects.

I'm sorry but to say that the american federal reserve's interest rates don't directly effect the RBA's monetary decision making isn't correct.

History gives us plenty of examples to illustrate the point.

2008 is the most recent example of the interest rates moving quickly in the same direction.

federal reserve interest rate chart.

Reserve bank of australia interest rate chart.


Also in the 1990's we saw dramatic moves in interest rates here are the charts.
Federal reserve interest rates chart.


Reserve bank of australia interest rate chart.



Sources
https://tradingeconomics.com
https://www.rba.gov.au/monetary-policy/about.html