A lot of people will recommend getting a uke from musicguymic's eBay store:
http://stores.shop.ebay.com.au/Musicguymics-Room
(goto the later pages for more affordable ukes).
Inexpensive ukes around the $100 mark often come with a bad set-up from the factory. The string height may be too high and the intonation may be off, which needs some experienced hands to adjust.
The reason why Musicguymic is so popular, even for overseas customers, is that he "sets up" each uke professionally, so that even the cheap ukes are well set up and comfortable to play. This is very much worth it - it is very annoying to learn on a poorly setup uke.
But for a beginner living in Australia, the shipping prices may be daunting.
Within Australia, I have found one inexpensive line of ukes that have a great set-up out-of-the-box. Keep an eye out for the Legacy brand ukes with spruce tops (either solid or laminate).
Every music store I have visited so far was able to order one in from their catalogue (if they don't already have it in stock.), and they are very good value. Comfortable and low action, and good sound.
Here's their website:
http://legacymusic.com.au/products/?id=6
Their "premium" series are very good quality. And since you're ordering through a music store, no shipping charges to pay!
Their "premium" soprano with laminate spruce top is just $99.99
http://legacymusic.com.au/products/index.cfm?action=view&id=59
Just about $49 more for a solid-top... and a bit more to add an active pickup.
Or if you want a Tenor:
http://legacymusic.com.au/products/index.cfm?action=view&id=60
If you're settling for a cheap $30 uke, the Legacy coloured sopranos are much better quality than Mahalo's $30 uke.
http://legacymusic.com.au/products/index.cfm?action=view&id=58
These are like the Australian's Dolphin substitute
One recommendation is to change the strings once u get it (Aquilas are good, its often cheaper to order Aquilas online if you're in Australia). They come with GHS strings, which don't bring out the best tone in most ukes.
They're very light on the fingers though, which could be a good thing for a beginner
As they're an Australian-run brand (though made in China), it is easier to get warranty/replacements within Australia.
I did when my Legacy Baritone had faulty tuners last year - I just returned it to the music store and they ordered in a brand new one for me
No problems since!