Before doing anything dramatic, see if your new router does a cashing DNS server where the local hosts doing DHCP get their hostnames assigned in the DNS and remote host names get forwarded to your ISP DNS server.
Then change your fixed IP address to use hostname or hostname.local.
Once you've used a router with this feature you'll never be satisfied with one that lacks it again.
Unfortanately few IP cameras have a proper hostname or implement the DHCP and/or AHAVI protocols correctly so when you change routers you'll have to lock the MAC address to the IP the camera uses.
To minimize the hassle, first off change your router to make the 198.168.xxx.yyy
match what you are using now, where xxx (usually 0,1or2) is the subnet and yyy is the router default address (usually 1, but my U-Verse router uses 254 and can't be changed as far as I can tell). Normally this doesn't matter as its what DHCP sets as the "default gateway".
If I boot a fresh Pi or Beaglebone on my router I can find its IP by doing ping pi.local or ping beaglebone.local Once I've given them a unique hostname I hever have to worry about what the actual IP address is.
If you've read through the above, my simple suggestion is to make sure the new router is 192.168.1.yyy I've never seen one that can't be changed unless provided by your ISP.
Then lock the MAC address of the Mosquitto broker Pi to 192.168.1.124