This is “normal” level of activity but QNAP is not being a good netizen.
The standard DNS setup on QTS uses a dnsmasq instance with caching disabled - so every time an application (e.g. QNAP store, connectivity checks, firmware update checker, etc.) needs to connect it fires a dns query. They also use a very low TTL on their DNS entries (60 seconds if I remember correctly).
In addition, if your NAS has more than one network interface it sends its DNS request to every interface. If you have IPv6 on your network multiply all the queries by 2 to account for the AAAA queries.
For starters it would make a difference if they enabled caching on dnsmasq and increased their TTLs to something like 30 minutes or more.