Applying for PhD programs before finishing your honours, when admission requires a first or high second honours? I want to apply to a bunch of PhD programs, particularly ones in Australia, Singapore and Hong Kong. All of these list a "High honours degree" for admission into their programs.

I will be finishing my honours in November, and will almost certainly be getting first class. The problem is that I'd like to apply to these programs before finishing in order to be eligible for certain scholarships. 

Is it normal for applicants to apply for a PhD program while still finishing their honours year, even when a high honours is specifically stated in the admission requirements?

If it matters, my transcript is all A's or A+ for every year except my first year, and all A+ for my 5 honours courses I've taken, with 3 left to go this semester.
Yes.  Typically applicants apply for a PhD program before completing the prerequisites.