Lioness pregnancies usually last around four months or so. Sometimes a bit less than that.
Kion and the various cub appearances in the films look more or less like 3-4 month year olds.
The sequel creates a bit of wonkiness with ages, though, so it's uncertain if the franchise really bothers to follow realistic lion aging all that much. If we're to believe Kovu(and, by extension of being in the same litter, Vitani) was really around for Scar to choose him as his successor, then he and his sister would be at least 7 or 8 months old at the earliest by the time Kovu meets Kiara. And yet... they're made to look exactly the same age. It's either because DisneyToons didn't really think about it too much, or they knew the age discrepancy but wanted to avoid things looking a bit awkward between Kiara and a lion cub that would already be twice her size(most likely this, given some deleted scenes involving Kiara's presentation as a baby and the Outlander kids witnessing it).
It's interesting to note the first film was originally going to put that "Kenya, 2 Years Later" earlier on in production after the time skip mid-way. It was probably around the time Simba still had that younger looking design with the mane all spiky looking, as shown in some
concept art and
old pencil tests. His mane still looks a bit more full than what would be expected, but you could probably buy it compared to the more finalized and blatantly more full grown adult design.