Andalites seem to have a longer life span than humans - although that's relative, since they go by a different calendar, obviously. Still, I think that Andalites likely develop faster than human infants. As you mentioned, Alic, their arms are probably too weak to hold their infants, and as they require movement to eat they probably learn to walk almost immediately after birth. Which isn't so uncommon, really. Their first few months of life they are obviously going to be unsteady and wobbly, and therefore restricted to the scoop. I'm thinking that their tail blades also grow in after birth (like humans with teeth), as that would wreak havoc on a mother's womb.
Intellectually they seem to mature fairly quickly as well. The height of human society is simple to Ax, and he often comments that a mere child could do what adult humans can do. Obviously some of this is due to the fact that Andalites have had more time to develop scientifically, but some of it also could be attributed to the speed at which they learn. If young children can do advanced math (by human terms), then that says a lot for their brain capacity.