There are two things you can do here.
First of all, it is possible to change the underlying document of a Q&A. If you start editing a Q&A and then navigate to “File”, you will see a button that says “Change document underlying this Q&A”. Clicking this button will let you choose a new document that will be used for this Q&A, without changing any cards or change sets you created. You could use this feature to replace the underlying document of one of the Q&As (maybe the most elaborate Q&A) with the binder you just created.
Another important feature you can use to save time with this process is the “import cards” feature. This can be accessed in the “Edit” section of the Design Q&A mode. You can change one of the panes (e.g. the “Changes” or “Base document” pane) to the “Import” pane (check out the relevant help page as well). It will then let you navigate to another Q&A and offer you the possibility to import existing cards of another Q&A into the Q&A you are currently editing. This makes it easy to re-use cards and/or change sets that you created for another Q&A.
An important distinction to be made here is that you can both import a card and create a proxy to an existing card. The first option, importing, creates a separate copy of the card which you can freely edit in your new Q&A without affecting the original Q&A. However, creating a proxy does the opposite: this imports the existing card into your new Q&A, which will remain linked to the card as it exists in the original Q&A. Any changes made there will also be made in this new Q&A. That also means that you will not be able to edit the card itself in this new Q&A. So carefully consider whether you want to import/copy the card or make a proxy to it. If you would want to delete the separate Q&As in the future, it will be better to import/copy it instead of creating a proxy.
A combination of both of the features described above will be best to make sure you don’t have to start all over again with an entirely new Q&A for your new binder.
I hope this helps.