For a first gun you can pick up a nice single shot .22 for around $120. Even comes with a pink, blue, or "camo" stock.
I could make several arguments that it would even be safer than this gun since it is a single shot, and it's a "real" gun and no one will mistake it for a toy with real bullets in it.
My 5 year old has shot my .22 and she got a kick out of it. Since she's starting on the real thing there won't be any bad habits learned about safety. High powered air rifle or not, it's not as dangerous as the genuine article, I doubt if it will shoot through walls, or even windows.
For squirrels and flying rats this would be better, you miss with a .22 in your semi suburban back yard and you're hitting something pretty hard. Missing with this seems a lot safer.
As a back yard plinker, it's ideal. Learn on a real gun at the range and then work on technique with this, maybe.