Sorry! Misunderstood you 
Yes, you could launch a .com.au but even if you have created Australian content I'd probably still be inclined to implement rel-alternate-hreflang annotations in your sitemaps; as the content will still likely be very similar.
The only issue with this is that your new domain won't have much in the way of link equity so it still might not rank without some link building effort on your part.
A further alternative would be to get yourself a generic domain like a .com and split into subfolders - /uk and /au. You'd then only have one site to build links to rather than two...
However the process of migrating from your .co.uk to your .com (and the potential to lose rankings whilst the search engines figure out what you're doing) might make this option unattractive.
I guess I'm saying launching the .com.au is probably quicker, cleaner and less risky but be aware you'll probably need to do some link building too.
I hope this helps,
Hannah