It seems this question would mostly attract opinions as answers - to get something objective you'd probably have to do a focus group with the types of people who would donate to you.
It's also a branding question, not foremost a web question.
But for what it's worth, as a fellow Aussie, I'd trust a .org.au before a .com, particularly if I hadn't heard of the charity before. It'd be much less common to have a bogus website set up with a .org.au domain.
In your case, I've heard of White Wreath before, so as long as it was clear to me that a .com was your official website (which it would be clear if I came from merchandise, or otherwise if I did a quick Google to see what ranks first), having a .com wouldn't affect my decision to donate.
If I hadn't heard of White Wreath before, then I would definitely trust you more seeing a .org.au domain. It'd also communicate that you were a home grown charity, and not an arm of a larger global entity, and therefore would make me likely to believe more of my money is staying local, helping a local project.
That also makes it a branding question: do you want to market to donors who already know you, or is this part of a bigger marketing push?
In regards to the merchandise, I wouldn't worry. Redirect the site, update the merchandise, in several years there'll be none of the .com stuff.
In summary, for Australian organisations - and similarly for Australian business with .com.au - I'd always say, use the .au :)