Advantages of delaying/accelerating PhD application
The academic year does start around September in the USA and I think most European countries.  At least in Europe, this doesn't necessarily mean that you would have to start your PhD in September.  For example, I did my PhD in the UK and started in June.

Note that your 'competitors' won't have finished their degree yet either when they are applying.  They will be slightly further along, having already started their final year, but not significantly so, I think.

Is cramming the rest of your undergraduate degree into one semester less at all a realistic option?

I do think you are likely to get stronger letters of recommendation once you are in your final year, because you will have been doing more advanced work and will probably have closer contacts with faculty.

I don't think that having some time between your honours year and your PhD is necessarily a bad idea.  My husband started his PhD only two weeks after finishing his MSc, and he really could have done with more of a break.  I had almost a year between my MSc and PhD, but I spent six months of that doing research.

One of my friends from Australia managed to get part-time teaching work at his undergraduate university until he went to the UK for his PhD.  Or if money isn't too much of an issue, you could take the opportunity to go travelling.

EDIT:  I'd just like to add, along the lines of Dave Clarke's comment, that you should bear in mind that your honours year will likely be a lot more challenging than previous years, and so 'accelerating' this year might turn out to be a bad idea.  I certainly worked harder in my fourth year of university (honours in New Zealand, so quite a similar system to Australia) than I have in any year since.