A switch would have been a better solution but What you have should work.
The 2 routers need to be in different subnets and route between them. Put the new router LAN back to 192.168.0.x . Connect a LAN interface of your old router to the WAN interface of the new router.
You will not be able to manage the new router from the WAN interface (old router side) unless you have turned this feature on so connect a computer to the LAN interface of the new router and configure it on http://192.168.0.x check connectivity from the management PC to the old router with “ping 192.168.1.254”
You can let the new router pick up a DHCP address from the old one if all you want is outbound internet. The static address 192.168.1.10 that you have assigned is likely to be within the DHCP range of the old router so you may get an IP conflict if you use that without modifying the DHCP scope of the old router to exclude the address you have used.