Twitch today confirmed that Prime subscribers “get up to 12 months of access to Nintendo Switch Online at no extra cost.” This is done by first claiming a 3-month Nintendo Switch Online offer now, and then claiming a 9-month offer at a later date.
The offer is available in certain countries only; Australia is on that list, so redeem away. You can do so here.
There’s a catch, of course — the Nintendo Switch Online membership will convert to a normal paid membership after this offer period expires. You’ll need a credit card or PayPal account to link to Nintendo Switch Online as a result.