Can I set up VAT on QBO without a registration number? How do I deal with transactions while I'm waiting for tehe registration number?

Your concern ends here, @AKT.

The registration number is required when setting up VAT in QuickBooks Online (QBO). Since it hasn't been issued by HMRC yet, I suggest waiting for it. 

I understand your client needs to start charging VAT on December 1st. However, QuickBooks needs the VAT registration number to complete the setup. Once you received the registration number, you can follow the steps below to set up VAT:

1. Sign in to your QBO account.
2. Click Taxes from the left menu, then select Set up VAT.
3. Select the beginning month of your current VAT period.
4. Choose your filing frequency. Then, select your VAT accounting scheme.
5. Enter your VAT registration number. If your business is entitled, choose the Flat Rate Scheme (FRS) checkbox.​
6. Click Save.

I'm adding this article for more guidance: Set up and edit VAT settings, codes, and rates.

Once you're ready to submit your VAT return, you can check out this article for the detailed steps and information: Submit a VAT return in QuickBooks Online.

I'm still open to your replies, @AKT. Please let me know if you need further assistance setting up VAT in QBO. I'll be standing by for your response.