I have been experimenting with playing a child character, and found several mods that make this possible.
Custom Playable Children - is the base mod to use. It is not perfect. You start the game with a new character as normal. With the mod activated you will see new presets to chose from in the regular list. They are basically copies of the vanilla child faces, with several options for hair color and eye color. They look a little weird, especially the eyebrows, because at this point your character is still the normal race and size.
So you pick a preset and exit character creation. Then you open the console and use the setrace command to change to the mod's new child race. You don't use the vanilla child race because it causes CTDs. Then you use the setscale command to shrink yourself down to child-size. Now your eyebrows look a lot more normal.
It works pretty well. The only issues I have found are that lipstick does not work correctly, and the eyes look a little odd. With lipstick, as soon as you select it the color is all black. But you can change to the other colors normally. However, the lipstick color does not line up with the lips, so it only covers the upper lip, and the skin above it. This is probably a side-effect of either the scaling or new race. The eye issue seems to be the lower eyelash also looks too high, so it is going across the lower part of the eyeball. But it is only really noticeable if you zoom in really close.
Otherwise the mod does add custom hairs and eyes specifically for the child character. The vanilla and Azar hairs do not fit the child-size heads. It even allows you to play a ghoul child, which I thought was a really nice touch.
Hair For Children - adds child-sized versions of all the vanilla hair styles. It works fine with Custom Playable Children.
Higher Female Protagonist Voice = This mod takes the vanilla voice files and changes the pitch up, to make the voice sound higher and thinner. There are several different options to chose from, with different levels of pitch change. You can only use one at a time.
It is big, really big, since it is every character sound file in the game. So it will take a while to download. There are also extra downloads for the dlcs. It comes in a .bsa file. The problem with this is that the game will ignore this particular one unless you add it's name to the .ini file. The only problem with this is that if you decide to delete the mod, you are also going to need to remove that from the .ini file. Which you might forget.
So you can do what I did, and open the .bsa with
B.A.E. - Bethesda Archive Extractor, and extract all the loose files into your game folder. The good thing about this is that you don't need the .esp file doing it this way. It works as a standard replacer, the same as a texture replacer would.
So far I tried out the U Voice, which is the highest. It sounds good, much more like a child, but there is a lot of distortion at times. The modder themself warns about this. So I am going to give the next higher voice a try.
Any Terminal At Any Height - this makes using terminals work with a child. The problem is that when you are little (or big) you cannot use terminals! I found this out the hard way. My child character is so short that when I tried using a terminal my point of view was so far down that I could not see the screen. So it was unusable. This mod fixes that.
So far it is going ok. I think my character - Ariel - is runs/walks a little slower than normal. This would be in keeping with Skyrim, where the taller races like Altmer actually can jump farther and run faster than the other races. I might try using the console to increase my movement speed. I don't know for sure.
Ariel is also definitely lower to the ground when in first person. That is a little odd. But it is how it should be.