Been trying to hunt down a solution to this also.
Putting aside the streaming websites that have been mentioned in other threads. (I don't have any links on hand, others may want to contribute this).
I have discovered a way of watching AFL Live full screen on desktop. With all of the controversy of the pathetic AFL app on iPad showing iPhone size footage, a clever fuka (technical term) has released a plugin for Kodi.
So yes, you'll need a little knowledge of computers (or at very least be able to follow instructions). Install Kodi on your desktop (just do a google search).
Then install inside kodi the AU catchup TV plugin. In there (yes there are step by step instructions) you can add AFL Live app and others like abc catch up, sbs, channel 7 etc.
Now to be able to watch the AFL Live app, its just like using the iPad app, you need an account and pay for the match. The benefit obviously is to 1, watch on a big screen/monitor, 2, push/airplay to your bigscreen TV (yet to test personally).
I am also yet to try this with a live match as I only installed all this yesterday, however I tested a replay of our first JTL game and the quality was excellent on a 27" 5k imac.
Link to the AFL live plugin:
Catch-up TV AU repository for XBMC/Kodi:
UPDATE Tested airplay to appletv, it works. Audio synced with the video, there was some frame drop though. I'm not sure if that was a airplay issue or a streaming issue. I'm thinking more airplay as I didn't notice such frame drops on the desktop.
Next step is to test a live game.