If you're looking for a way to do this from a web page, consider making an applet that pings servername.everquest2.com when the page loads and parses the result. If I recall, server down will return server unreachable or somesuch. (Overdoing this might be bad for your server, mmmmkay?)
If you're looking for something from within eq2 this might just be what you're looking for. Scroll all the way down.
Connection Stats Window
* We've added a connection statistics window which will show your ping, bytes per second, frames per second and packet loss. The default key to toggle this window is F11.