I hate this, same thing happend to my 1 week old Honda a few years ago. I never did get the scratches out (100+lb dog
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Since this is a small dog I have to assume the scratches aren't too deep. Essentially what you need to do is level the paint around the scratches to make them less visible, as Ferdman already suggested I would start with a quality hand polish first and step up to a more agressive product as needed. The Griots is excellent and Meguiars Scratch X might work ok. Otherwise Meguiars Dual Action Cleaner Polish with a Porter Cable works very well followed by a ligther polish.
If you feel it's over your head bring it to a body shop and ask them to buff it out, they shouldn't charge too much for that.