In the Great & Small Quick Start rules as they're currently written, each species of animal receives a fixed number of hit points per level, modified by the roll of their niche dice. I derived the hit point values through more or less straight conversion of the animal stats (or stats of a similar creature) from the Basic/Expert rules, the Rules Cyclopedia, or some other basic edition resource or retroclone. I gave each animal maximum possible hit points at 0-level, followed by an average value of their listed Hit Die type each consecutive level thereafter.
Tying hit point progression to species in this manner is just an iteration of the race-as-class concept from basic editions, in which dwarf, elf, and halfling were classes unto themselves. But the method produces inconsistent results, giving divergent hp progressions to species of roughly equal profile (such as rabbits and small cats). Some players may find this approach illogical and unsatisfactory.
Therefore, I've been toying with the idea of tying hit point progression to Size Category rather than species or niche. In this scheme, rather than receiving a fixed amount of hp + niche die result per level, all characters roll for hit points per level on a die type tied to their Size.
Size determines type of die rolled for hit points per level according to the following table:
Hit Dice Per Level By Size Category (Zocchi Dice Progression)
Fine: 1 hp
Hit Dice Per Level By Size Category (Standard Dice Progression)