I don't use unifi routers, so I can't comment on their setup. I do use their wifi stuff though.
The main reason you would rely on your gateway to forward/relay DNS requests is because you're trying some type of monitoring/blocking setup in the router and it needs that for the filtering insight. If you aren't filtering there, then don't add the relay function to the router's list of responsibilities, let the clients query the provider's DNS directly.
In order for the local gateway's filtering to be successsful, you'd need it to also block all other DNS requests to outside servers. If you don't, this filtering setup is easily bypassed by a client specifying an outside DNS server. I would note that this is a common tactic for infected systems, change the preferred DNS to complete/maintain the infection.
If you want DNS filtering, I'd suggest looking at OpenDNS's free "Home" solution, you can use it with custom lists. But as I mentioned above, you should also block all other DNS traffic that isn't to your desired server.
For my home stuff, I opt for a slightly more advanced design. I allow DNS to my OpenDNS resolvers and I redirect all other DNS traffic to outside servers (like 8.8.8.8 and 1.1.1.1) to my OpenDNS servers. So, that ChromeCast HDMI dongle that really really wants to use 8.8.8.8, disregarding what it got in DHCP, will still get an answer - but it's from my OpenDNS solution because I destination NAT'd all DNS traffic to my preferred server.
