Nice, looks like solid coding altogether. Here are a few thoughts:

It doesn't really matter in a simple program like this, but in general you shouldn't open files sooner than you need them, it wastes memory. You could open the file after the diary entry is entered. Or, you could open the file beforehand and use an implementation like this:

#files are open already
print "Write to diary. Type quit when finished.";
while (($_=<STDIN>) != "quit\n")
   {
   print FILE $_;
   print DIARY $_;
   }
[download]

Now you aren't reading the entire diary entry into memory, only one line at once. Like I said earlier, it is trivial in this program. But it will pay later to think about things like this. Overall, though, it looks good. I've seen plenty of code created for commercial use that is a lot worse than this.

When's the last time you used duct tape on a duct? --Larry Wall