We are purchasing components with purchase orders and assembling into finished goods. Can I do this with QuickBooks plus?

QB Online doesn't provide any assembly feature. You may have 2 options:

1. Having an assembly app to integrate with your QBO account.

2. Switching to QB Desktop Premier or Enterprise edition. Deploy a private cloud if required.

Is there a way to transfer accounts and inventory over to the desktop version. 

Is there a way to transfer accounts and inventory over the the desktop premier version?

For your reference

https://quickbooks.intuit.com/learn-support/en-us/import-or-export-data-files/export-and-convert-you...

If you hit the wall, you may 2 options to migrate data from QB Online 

1. Utilize a migration tool. i.e TPExporter for Online, TPImporter for Desktop

https:// transactionpro.grsm.io/qbo

2. Purchase a 3rd party conversion service.