I recently purchased a new 13" MacBook Air to replace my older 17" MacBook Pro.
How can I move my iTunes library to my new MBA?
I also plan on purchasing a new iPhone in the next month or so. Can I move my songs from my iPod to that too?
Easy. Copy it from the old Mac to the new one.
There are a variety of techniques including Setup Assistant (as soon as you get your new MacBook Air, it will ask you if you want to transfer information from another computer), Migration Assistant (if you elect to transfer information later), enabling file sharing between the two computers, or copying your music to a flash drive or other storage device followed by importing it to iTunes.
Once your music library and everything else you want to transfer from the MacBook Pro resides on the new MBA, sync your iPod to the MBA. Sync the iPhone too when you get it, and they will both have identical iTunes music libraries.