QuickBooks Self-Employed version can only track Self-Assessment income (ITSA) alone, and it doesn't support VAT tracking at this time, Info2243.
Aside from that, QBSE isn't a registered platform for Making Tax Digital (MTD) compliance. This means we cannot directly submit VAT returns to HMRC through QuickBooks Self-Employed.
As of the moment, we can generate a Tax Summary or Tax Details report in QuickBooks to convert and download the file to CSV. See this reference below:

After that, manually enter the details directly into the HMRC portal to file your VAT return.
If you want to automate the VAT submission process, you'll need to upgrade to QuickBooks Online (QBO) to do this. However, please note that you must be VAT registered and comply with the Making Tax Digital (MTD) requirements.
If you need more guidance, please add your comment below.