Tim,
I doubt whether many people on the Forum have been in your exact position, so maybe you will only be given general advice - but who knows?
You shouldn't really think about applying for a visa until you have known her for at least a year: the Embassy are not impressed by speed! And you need to be gathering proof of relationship: photos, communications etc. Your divorce is going to take some time, even if it is supposedly strightforward, so use that time to build up the relationship and to understand the application procedure and requirements, which have been covered by many posts on this forum and also on Pete's site. And, money and time permitting, use it to visit her as much as possible.
Have you had a look at the visa application form? You may need to think how you will fill in details about her residence and work in HK.... How long have you actually known her? If it is not long, perhaps you should not think about a formal proposal of marriage on your next trip: the Embassy are likely to ask about how long you knew each other before you decided to get married, and if it's only a few weeks, I think they would seize on that as being unconvincing as regards yours being a genuine relationship.
So, take your time over this, read all you can on this Forum, Pete's site, and the official immigration sites, including the British Embassy in Manila, and UKVACS. There are a lot of success stories from people on this Forum, so keep asking questions!
Ivor and Mel