I recently started a new campaign (D&D 4e) with my son. In order to make it a little easier on him, I allowed him to have a companion character (per the DMG2). Being a ten-year-old, he wanted a dragon. As a companion. At level one. sigh
So, I wrote down the stat-block for a fire beetle and told him it was a baby dragon. The dragonling can fly a foot or two off the ground, but he's afraid of heights, and too small to carry anyone. That seems to have satisfied him.
Oh, and he wanted a blue dragon, so it does a "Spark Spray" (lightning damage) rather than a fire spray.
During play, the question came up -- do companions get Action Points? PCs get action points. Some monsters get action points. Companions are somewhere in the middle, and they do get a full share of the XP.
I'm leaning towards giving the baby dragon an Action Point. This is mostly because I'm going easy on the kid, in order to keep him interested.