I purchased the song "What does the fox say?" on Google Play.
I am trying to play this song on my iPod but it won't let me move it from my iTunes library to the device.
What's the problem?
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Install this app(Google Play Music) on your iPod. You should be able to sign-in with your Google-ID, download the songs you own, and play them.
I don't know the application, nor do I use Google Play Music, but I expect this to work.
If you want to play it in your iTunes on your iPod you can go to Google Play and go to your music. The track will be listed there. Right click it and click download. Drag-and-drop the track into your iTunes and Sync your iPod.