When it comes to foreign exchange carry trade strategy, the definition is straightforward: an investor borrows 1 US-\$in the US (low interest country) and invests that \$1 to AU (high interest country). By doing so, his dollar denominated return will be:

$$R_{t+1}^i = \frac{S_{t+1}^i}{S_{t}^i}(1+r_{f,t}^i) - (1+r_{f,t}^{US})$$

where $$S_t$$ is the exchange rate today, and $$S_{t+1}$$ is the exchange rate at time $$t+1$$, $$r_f$$ is the risk-free interest rate in the corresponding country.

However, the literature on the subject suggests using synthesized carry trade using forward contract, that is, buying forward AU currency at time $$t$$ with delivery for $$t+1$$, and then the difference between spot rate at time $$t+1$$ and forward rate would be the return to the investor:

$$R_{t+1}^i = \frac{S_{t+1}^i}{F_{t,t+1}^i} -1 = \frac{S_{t+1}^i (1+r_{f,t}^i)}{S_{t}^i (1+r_{f,t}^{US})} -1$$

Apparently, the latter is a common way FX carry trade is actually implemented.