Yes, you can import your QuickBooks Desktop to Online, @peterelwood.
In your case, you'll need to download an updated version of QuickBooks Desktop so you can move your file to QuickBooks Online. Make sure to create a backup copy of your file first. Let me walk you through the process.
I do not want to transfer all my companies to online quick books. I want to keep my other companies on my old version of Quickbooks, which is “Quickbook Pro 2007.
I only need one company transferred to online version.
Call and ask Intuit Data Service to convert your data file to one of recent versions, open it on trial license of Pro 2020, and self-migrate it to QBO. Otherwise, you have to purchase a 3rd party comversion service to get the converted QBW file ready to open on Pro 2020.