As Sarah Dickinson recently mentioned at DNS-OARC 27 in San Jose, CA, https://indico.dns-oarc.net/event/27/session/4/contribution/20, there is a work in progress for a TLS DNS Proxy for the Apple iPhone/iPad running iOS 11 and above. This uses the new DNS Proxy Network Extension and, when enabled, all DNS requests will be sent to a resolver over TLS.

I expect this new DNS Network Extension to be available for macOS in a future release as well.

Check back here in a bit to see the status and sign up for beta testing.

UPDATE:

After receiving the following message on the Console, it appears that the only way to use the new DNS Proxy Network Extension in iOS 11 is through Mobile Device Management (MDM) Tools as a supervised device. This makes it impossible to install for the average user through the App Store.

Therefore, I am suspending this effort until this extension is more useful to a wider audience.

Oct  5 17:29:26 iPhone nehelper(NetworkExtension)[99] <Error>: -[NEHelperConfigurationManager:562  Warning: allowing creation/modification of a DNS proxy configuration on non-supervised device because the requesting app (DNS-TLS) is a development version. This will not be allowed for the production version of DNS-TLS

UPDATE 2:

An Apple representative confirmed this is currently only for supervised devices but he seems to indicate they are considering opening this up to all devices but with no assurances or timeline:

I’ve just confirmed that, as things currently stand, NEDNSProxyProvider is limited to supervised devices.  We have a bug on file (r. 34843801) requesting that this restriction be lifted.  I suspect that this will happen but, as per usual, I can’t make any specific promises about that, or about the timeline for this change.  It certainly wouldn’t hurt for each of you to file your own bug describing your use case, how this restriction is affecting you, and what workarounds you’ve resorted to.