So, I found out some details for myself.
Camel did NOT successfully connect to SMPPSim (I detected it using log:tail in the karaf console)
Once the connection was successfully established, it worked out of the box: Just use TextMessage for the ActiveMQ-Queue and the body of the TextMessage will be the body/message-text of the SMS. Set headers for the Queue and camel will forward it as headers for the SMSC-Server. Then there are the camel-special-headers that it uses for the configuration, as documented. For example:
request.Properties["CamelSmppDestAddr"] = number.ToString();
Plus: I found out how to install camel:smpp without using karaf and just using ApacheMQ with the camel plugin: Download the camel-smpp-**.jar file (in my case camel-smpp-2.12.1.jar) and put it in the [activemq-root-folder]/lib/camel/ folder. The Jsmpp-dependency was missing; Search for it (as of now: jsmpp-2.1.0) and put it directly in the lib folder!