I haven't been back to Perth since the end of 2013, and I know there's been a huge trend in healthy eating since then (which tends to include lots of veg friendly stuff), but I posted about a few options in Perth/Freo on my blog - there's PAWS in the CBD, The Raw Kitchen and Juicy Beetroot in Freo (amongst many other options).
As for Busselton not sure about in the town, but I'm sure you'll prob go around the area (the south is beautiful - within reach of Busselton are gorgeous spots like Dunsborough, Margaret River, and more) In Dunsborough there's a place called Samudra which was cool, and if you happen to stop in Mandurah on the way down, there's a place called Taste and Graze with vegan options, and then in Bunbury an amazing place called the Plant Organic which had awesome raw cakes. The happy cow app is pretty good for it, but as I said, I posted about a few places on my blog if you want to take a look - http://littleveganbear.com/rest-of-australia/
Enjoy! I love W.A :)