I appreciate the update you've provided above about which QuickBooks software you prefer in handing your payroll data, @damjan. I'm here to share further details about this.

Currently, the QuickBooks Online (QBO) software uses its cloud-based solution in storing data (i.e., payroll). With this, using a private cloud (server) to store your database isn't an option. 

When your IT manager considers the possibility to switch from QuickBooks Desktop (QBDT) to QBO, you can help them decide by providing some information on what to expect when doing so. Once they agreed, you can check out this article on how to import your QBDT company file to QBO: Move your QuickBooks Desktop file to QuickBooks Online.

Additionally, each version of QuickBooks is designed to address specific business needs. To give you an overview of each product, service, and version of QuickBooks, I'd recommend checking out this article: See which version of QuickBooks is right for you.

Let me know how it goes in the comments below. If you have other concerns about handling your payroll data and company file in QuickBooks, I'm just around to help. Take care always.