How can I ensure DNS queries from H series firewall could route through the VPN to peer site?

Zyxel_Stanley

The DNS query packets initialed firewall(local out) to remote VPN gateway via VPN tunnel, you need to use a Route-Based VPN and additional policy route rule.

Since the Route-Based VPN will auto generate a Virtual Tunnel Interface automatically. Then you can create additional policy or static route to by pass the traffic.