Below is my config for anyone else that is trying to get this working:
mjarends@router# show system name-server name-server 127.0.0.1 mjarends@router# show system domain-name domain-name mydomain.name
mjarends@router# show service dhcp-server disabled
disabled false
mjarends@router# show service dhcp-server use-dnsmasq
use-dnsmasq enable
mjarends@router# show service dhcp-server shared-network-name LAN1 subnet 192.168.1.0/24 dns-server dns-server 192.168.1.1 mjarends@router# show service dhcp-server shared-network-name LAN1 subnet 192.168.1.0/24 domain-name domain-name mydomain.name mjarends@router# show service dns forwarding name-server name-server 208.67.222.222 name-server 208.67.220.220