A moose would feed your tribe a lot longer than a rabbit. Once you have established a solid harvesting process, it is much more efficient to sustain a population from larger animals.
Tribes, harvesting aren't those sound more like possible with modern social structures? I expect them to form in the latter part of the 1.5 million years period. In the graph from the tweet shows delicacy(!) was elephant around 1 million years ago.
