If there is currently support for Mulesoft 3.0-3.8 I assume that 3.9 is on the Dynatrace roadmap for support. In the link below you can see that they have begun working on the Java agent to capture headers in Mule 3.9.0:
Here is some information on special modifications you have to do to monitor Mule applications. Other than what is listed here you should not have to other configuration changes to the regular agent installation process.
Hope this helps,