In an ideal world, you'd keep the sizing matching the growth of the tyke. However, they grow fast enough that most people can't afford the money or space to keep a acquire bikes of correct size at all times.
The usual compromise (in the US at least, especially in families which aren't made up of cyclists) is to buy a bike which is bigger than necessary for the kid, and let them ride it until its too small for them. This is easier to deal with for children cause they don't start out with all sorts of body pain and they don't ride long enough distances for form and stuff to matter. Young kids are also a case where riding a bso is okay, in my opinion; they're not with the bikes long enough for quality to matter in most cases, and its not like they're going to learn upkeep until they're early teenagers anyway.
It'd be fine for her to ride the 16" bike, but there is the question of how long the 16" bike will be a good fit for her. It might be better to wait for her to hit around 120 cm and then skip the 16" bike or something (this is what I did).