Did you get your a/p to register under the Worker Registration Scheme?

[FeatheredHeart]

Apparently they should if they're from Czech Republic, Estonia, Hungary, Latvia, Lithuania, Poland, Slovakia or Slovenia

needs to be done in the first month of work, but it seemed to be a formality to be approved, and it doesn't stop someone starting their job.

Your au pair doesn't need to be registered under the worker registration scheme since it isn't classed as work for the purposes of the worker registration scheme. If you want to issue her with a more formal contract of employment and are paying her at a higher weekly rate that takes her above the earnings threshold then you should.

Exactly what Treeesa said!
You don't register standard au pair under worker registration scheme.