I suggest you watch some Unity3D tutorials on YouTube or learn at http://unity3d.com/learn to get familiarized with Unity capabilities. You don't need to memorize them all, just see what it offers you so you can go back to it and use it once you need it.
I'm assuming the pet game you want is somewhat like Tamagotchi? If so, you can easily start off with default first-person player controller Unity offers, and just modify it to your needs. And also, you can first focus making the game as pc/mac/linux standalone, and once it's at finishing process, just add all the controls for mobile devices, or just do that on the run.
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