In the past few years there has been a growing desire to provide more built in functionality to protect user communications from eavesdropping. An example of this is DNS over HTTPS (DoH) which can be used to protect user privacy, confidentiality and against spoofing attacks. Since its first popularity in 2018 as used in browsers, there is much further study to test the effectiveness of DoH in protection schemes and whether it is possible to detect the protocol over the web. Detecting DoH traffic among normal web traffic is also a major challenge for network admins to allow filtering of malicious traffic flows. In this paper, we investigate machine learning classification to study the detection of DoH traffic and further analyze the key feature characteristics in the protocol behavior to help researchers build credibility in the DoH protocol detection. Our study reveals key features and statistical relationships among DoH test runs on the Alexa-recommended 100 most-used websites using three different DoH servers, showing up to 98% test accuracy in our built classifier.