A few days late but HELLO.
For games, I'd actually recommend learning the ins and outs of Unity3D's engine over OGRE3D (which is not a standalone games engine afaik). I've never seen Ogre3D pop up anywhere in my freelance line of work; it's generally unreal/unity these days in the indie market. There's so, so many tutorials and online resources revolving around Unity-- and it's free! Animal games are definitely possible-- I believe Lif was made in unity. But for ease and simplicity, do give it a try if your heart isn't set on Ogre! It may be a bit less daunting than learning multiple different packages.
(Feel free to correct me if I'm wrong; I just make the arts and textures. I've little coding knowledge at all!)