Welcome to the Community, @harvey-blackpugi.
I'd be glad to share with you some information about importing your Quicken data to QuickBooks Self-Employed (QBSE). Currently, the option to do the conversion between the two programs is unavailable since QBSE is a stand-alone product. You can only move your Quicken file to QuickBooks Online (QBO) and QuickBooks Desktop (QBDT).
You'll want to check some third-party apps that might help you in migrating information to QBSE. To do so, feel free to visit our QuickBooks Apps Store.
In case you want to import bank transactions into your QBSE account, you can easily do it using a CSV file.
Don't hesitate to reply to this post if you have other concerns with your Quicken data conversion to QBSE. I'll get back to you as soon as I can. Have a good one.