yes 3rd party support was allowed at a AIT case, but whether its been accepted by all case workers i don't know..
your problem is you have 13k savings which was a gift, and you have no job at the moment and are relying on your sister for accommodation, also you dont have any bank statements ? or pay slips. it doesn't look good does it ?
if i was you i would wait til your working and have some bank statements and pay slips,then you wouldn't have to mention where your savings came from, i think if you dont have any bank statesments your going to have to explain where your money came from ..
but you could apply, but it looks risky to me..