Well here's one little bit of help - I hope. I can't speak for Australians or Brits but at least here in the States, the word 'propose' is a tricky word to use when speaking about relationships with females.
If you said "I'm going to propose to her" here in the US, 99% of folks would interpret that to mean you are going to ask her to marry you. That doesn't sound like the case, from the rest of your description.
Does she smile a lot when the two of you speak? At some point when both of you are having fun talking, tell her that you really like the time you get to spend around her. It's the truth isn't it? Then add that the two of you should do more of it.
Maybe she'll agree enthusiastically and you ask her what she likes to do for fun. On the other hand, she may be cool to the idea, and maybe behave differently once she learns of your interest. In that case you've at least avoided the outright rejection of being told 'no.'
And by the way ... if you never act - if you never ask - the answer will always be no.
