Using the initial perl method (removing the loop), I've wrapped this up as an Applescript application attached to this post. When you run it, it will ask where to save the log, then run the ping every 60 seconds.

If you want to hardcode a file to write to, let me know and I'll walk you through modifying it to do so. This way this is a normal Mac app that can easily be added to startup. (Right click on the icon of it on the dock, go to options, open at login.