If you were using Settings >> Wi-Fi and the 'Advanced' option in your home WiFi network listing, try deleting it and then add it in again to see if the DNS options are changeable again.
You might also want to try installing an app like 'DNS Changer':
https://play.google.com/store/apps/details?id=com.burakgon.dnschanger&hl=en_US
Using an app like this might work out better for you if you connect to different WiFi networks on a frequent basis as it can be applied to any WiFi network you connect to. If you just change your home network entry in your Settings >> WiFi menu, the DNS change only applies to your home WiFi network, and if you change the DNS on your router, don't forget that only applies to when you're connected to your home network.
You mention Cloudfare's DNS offering ( 1.1.1.1 and 1.0.0.1 ) and offhand refer to Google's ( 8.8.8.8 and 8.8.8.4.4 ) but you might want to take a look at a couple of other public DNS services:
My preference is Quad9 ( 9.9.9.9 )
https://www.quad9.net/
There's also Cisco's OpenDNS (208.67.222.222 and 208.67.220.220), a good option if you want to have configurable settings
https://en.wikipedia.org/wiki/OpenDNS
These are all public DNS focused on security and/or privacy aspects. If you just want the
fastest DNS, try using this DNS Benchmark utility (it's a Windows exe but works well using WINE on Linux or MacOS):
https://www.grc.com/dns/benchmark.htm
Read the instructions carefully, that has a lot to do with getting a more accurate assessment (i.e. run the test when your home network is being used by other family members), and you'll probably want to do this two or three times in a day as your ISP's network will be under different loads depending on time of day. But this is a good way to find out what DNS services (public and commercial) that are available in your specific location. Personally I prefer to use a DNS service that's more security/privacy focused, and the speed is secondary as I'm willing to sacrifice the fractions of milliseconds difference.
