First significant house rule:
GOLDEN LION RULE: (Named for Jad-Bal-Ja in the Tarzan series): For important pets and animal companions, each time the owner levels, the creature gains a new hit die of the same type. Note that the Judge has final say as to what is a significant animal, but it generally revolves around whether or not the creature is participatory in the game.
I like this idea. This subject has been the center of discussion in my play testing group lately, but centered on familiars. How would your rule intersect with the rules for familiars, or would the Golden Lion rule only apply to non-familars? Or, is this something that falls under the 'Judge has final say' category?
That's not a bad idea, but I would increase the hit dice from 0-lvl to 1st lvl in the event that the creature is starting equipment. Remember that increases in hit dice just mean that the thing is going to survive longer; I am not suggesting an increase to damage, attack bonus, etc.
I was wondering at your reasons for not allowing some sort of increase in the saves and attacks? It stands to reason that if you want the critter to survive longer, then it should at least get some kind of advantage to saves. Just curious...