1) Change the application into something that you can be more familiar and have access to the packet easily. See the third tutorial for MyApp class (
http://www.nsnam.org/docs/tutorial/html/tracing.html?highlight=myapp) which is a simple application generating packets with a given rate. There you can find the SendPacket method and see where the packet is created. Before you send the packet, you can add the timestamp.
2) You can go and change the source code of UdpClient application and similarly find the SendPacket method and add the timestamp there. Since ns-3 is an open-source project, you can do it without any problem.