I wouldn't be surprised to see a young Elisa in Australia (e.g. under 18); but yes I'd expect her to come from the eastern or southern European origin communities.
Elise is unremarkable for an Australian under 40.
Alyse would get pronounced like Elise rather than Alice, even though it is a variation of Alice not Elizabeth. I'd be surprised to see it on an Australian older than 25.
Lisa is pretty but common. I'd be surprised to see it on an Australian younger than 25.
Eliza was the most common stand-alone nickname for Elizabeth in the baby name stats for most of the 90s.
https://nanowrimo.org/participants/christine-seaforth-finch
http://christineseaforthfinch.blogspot.com/