The detection part I think you're misunderstanding is that you need to compare what the machine is logging and what it's actually doing, by looking network traffic, etc. Looking for parallax, differences between the two.
It's amusing that you actually believe that you can 'check the logs' to detect all DoH being performed on the machine. Would you be willing to disclose your employer? "I can check the logs" sounds like something a naive systems administrator would say.
I'm glad that 'security' is your thing. The best thing about the internet is that you never know who you are talking to... Even when you meet people that wrote the parts of the operating system you're currently using.
Also feel free to Google me, creepy as it is, I’ve no idea why my specific employer would help this discussion in anyway.
PS the victims of solarwinds had dns and it didn’t help them. Expecting the attacker to use a known IOC or contact an obvious C&C domain is where the industry is at. My opinion is DoH will actually force blue teams to build systems that are effective. My chosen model is parallax. Known behavior, known states that can be checked.