Are you sure? With an appreciation in the Australian dollar, consumers would be more inclined to import as overseas products are relatively cheaper than domestic products. Also, as the Australian dollar appreciates, it effectively becomes less internationally competitive as countries can opt to import commodities from another country at a cheaper (because the exchange rate difference between $A and another's currency is wider).
This effect leads to less exports and more imports, worsening the terms of trade because we can now finance less imports with the same amount of exports.
Firstly, the terms of trade does not measure anything to do with volumes, so worrying about the short run or long run effects is a waste of time. The J-curve does not come into play here.
The ToT is:
XPI / MPI
Where MPI and XPI are the import and export price index respectively.
So this leads to what is a really interesting question. What happens to the ToT when the currency fluctuates?
In actual fact the answer is ambiguous. You cannot say either way because it depends on the nature of imports and exports within an economy.
For an appreciation, four combinations are possible:
1 - Import prices remain the same because they are expressed in Australian dollars (e.g. many contracts may be written in AUD)
2 - Import prices fall as the AUD is stronger, and imports are expressed in a foreign currency (e.g. we trade in USD when importing boeing aeroplanes).
3 - Export prices remain the same because australian companies continue to charge the same amount for their product (e.g. educational institutions do not charge foreign students a different price in AUD when the currency appreciates)
4 - Export prices fall because australian producers operate in global markets and have to accept a world price. With an appreciation, the world price expressed in some foreign currency - usually USD - is now less in terms of AUD (e.g. coal is sold at a world price; not a domestic price that suits Australian suppliers).
So as you can see it can either rise or fall. Import prices may fall, but then so can export prices. For australia an appreciation tends to reduce import prices by more than export prices, so an appreciation usually improves the terms of trade, however this effect is ambiguous.