I'm starting to have a similar problem with my DD3, even though she isn't even 5 year (5 in Sept), and starting school this year wasn't even an option. She has actually been getting teary and not wanting to go to preschool, saying "It's too boring!". It hasn't impacted her behaviour at preschool yet, although the teachers have noticed that she seems unsettled, not really interested in staying with any of the activities.
After speaking to the staff, they are now attempting to extend her a bit, to try nd get her interest back
And it can be a problem that last year of preschool with a lot of kids. With a single point of entry in most states, there are always going to be children who are ready well before the start of the next year rolls around.
Talk to the staff, work with them. Sounds like they already on top of it at the moment. The challenge is just keeping up with for the next 3 terms

Workbooks are great. You can get them covering all sorts of things - handwriting, letter recognition, maths starting right from counting 1-20 into real maths work, even things like colours and shapes, and patterns etc. They have sticker rewards, you can even get disney character ones etc to make them more fun.
Does the room at childcare have any computers? You can get some great educational games for kids. And they aren't expensive - EB games have all the learning ladder games for $10 each, which start at kinder level. Great for not only learning the skills like reading and maths, but also for the general computer skills. And again, fun for the kids.