When you saved the logo from the "official" site, , you probably saved the file as "doop.jpg" (since that's what the site calls it). The .jpg extension is a good indication that the image is in the JPEG format. If you don't see file extensions on your computer (Windows XP hides them by default), you can always right-click on any image on a Web page and select "Properties" or something similar; there should be a field in the Properties window called "Location" or "Address" or the like that will show you the URL of the image, which is http://www.doop.org/img/doop.jpg (as before, the .jpg extension is a good indicator that the image is a JPEG). So that original image is already compressed as a JPEG, and it will already have compression artifacts.
But that site doesn't seem to be an official Futurama site; it seems to be a fan site unrelated to Fox or any of its affiliates. So it's possible that there is an official Fox page that will have a PNG version of the DOOP logo (more likely you will find a GIF version, which can be losslessly converted to a PNG). But you'll have to do some searching. —