Can I move the HDD and keep the data from ASUSTOR NAS to another ASUSTOR NAS？

Yes。
ASUSTOR’s built-in system migration mechanism allows you to quickly upgrade from your current NAS model to a newer one by moving your original hard disks to a new NAS system. This function is also extremely useful in the unfortunate event of a system malfunction or failure. You only need to move your hard disks from one system to another without need for transferring data or re-installing the entire system.。

Steps:

Power off your NAS  -> move the HDD to a new ASUSTOR NAS  ->  Power on the new NAS.

For complete tutorial, please refer to ASUSTOR College

NAS 343: Introduction to System Migration