Groundcover sized Sedums would work with light foot traffic, full to mostly sun, well drained - i.e., pea gravelly loose soil.

Mazus takes light foot traffic and blooms in spring if it is in mostly shade. It dies back to dead in sun. I use it under my shade loving shrubs instead of mulch.

Neither of these need mowing and neither are toxic. Something you might want to consider with a toddler.

Birdsfoot trefoil and roots of rupturewort are toxic if eaten by little ones.

Nancy the nancedar

I have mazus in the sun and it does fine, but it's in amended soil. My only problem is that in the sun, certain weeds grow up through it, the worst one being that clover look-alike, wood sorrel. It is soft, though.

I love walking on wooley thyme! Great weed control and spreads like mad. really soft. I walk on it, kneel on it and if the patch is big enough I would probably sleep on it!