Hi Thermae, welcom to FT!
From what I know of, the limit is of a 90-day *consecutive* stay, never heard of the "90 days in 180" rule. In any case, I go in and out of Schengen all of the time, and in some periods of year definitely spend more than 90 days in the last 180-day-period in Schengen area. Never had any troubles for that.
In any case, even if such rule exists, it probably applies as "90 days in the last 180 days", so your 1-day stay in Copenhagen doesn't really matter. I don't think there would be discrete 180-day-period triggers, that would be just overly complicated.
Plus, you're Australian, so I don't think anyone would give you trouble

Enjoy Europe!
*Edit* Just googled a little:
There really appears to be the limitation, but as I said, I've never seen it enforced on me. And it does look up the *last* 180 days, not 180 days since the first entry into Schengen space. So, if you don't want to risk it (and really nothing might happen if you do), you might want to adjust your travel plans to spend 45 days in the UK, then do the non-schengen countries, and finish it off back in Schengen.