Could you not reuse the colours, e.g. using the purples for external AA?

I see what you mean and I agree.
I was working under a very restricted pallette, so when I wanted to use e.g. the darkest purple for the rabbit, I was left with none to AA those areas. 

There are tricks for these things, but the whole picture uses very "clean" colors, so I didn't want to use grey or blue or something like that.

You have nice AA in some parts and no AA in others, looks rather strange. I think the desk and the rabbit(?) in particular could use some more AA.

Also, don't be afraid to cut into your outlines with AA. It's not the "mathematical" thickenss of the outline that matters, but the overall impression. The outline looking right is more important than it actually being "right".