Each subnet has its own gateway. It will need to first go thru its own gateway 0.254 and then it will find the rest of the other network 1.x.
In order for machines on the 192.168.0.0 network to find the default gateway you need to do one of two things.
1. Install some routing software on a computer with two Ethernet cards so that machines on the 192.168.0.0 network can use that machine as their default gateway, then that machine would forward the packets on to the default gateway of the 192.168.1.0 subnet.
2. Configure the router and all the computers on both network to use a wider subnet mask so that the 192.168.0.0 and 192.168.1.0 subnets are one larger subnet. A Subnet mast of 255.255.240.0 should be more than wide enough. The you can configure all the machines on both networks to use 192.168.1.1 as the default gateway.