Eagar is already an Aussie (Aussie Mother), so could play for them anyway.
If he was looking to gain AU passport for playing he'd be shit outta luck, as he has played a youth A International, which rules him out of playing at National Level for anyone he doesn't already have a passport for (The Lia Clause).
He could switch as long as he was eligible to play for Aus when he played the youth games for NZ. Which sounds like he could be if his mum was born in Australia.
Only if he actually held Oz citizenship at the time (i think).