I´ve had a few very small guitar students begin lessons with a full sized acoustic or electric guitar. One child who was 9 could barely see over the top of the guitar body when he sat down and he unfortunately struggled with the large guitar and never looked comfortable.
Some of my students are as young as 4 years old as these young children absolutely need a smaller guitar. I had one student who had a full sized electric and couldn´t reach the end of the neck with his left hand. It was definitely a huge problem for him. Fortunately they make guitars of many different sizes. I loaned this student a 1/2 sized guitar and he is managing it very well.
Guitar is a challenge, it takes work and can be frustrating. Having a guitar that is too large can add to those frustrations. It takes a little while to feel comfortable with a guitar and having one your size certainly helps.
How guitars are measured
Guitars are either measured by over all length or on a scale. For instance you can buy a full sized guitar or a 1/4 scale guitar.
The scale is the distance between the nut(end of the neck at the head stock) and the bridge. This is the part of the string that vibrates when you pick it.
Some guitars have a smaller body or a shorter overall length but are still considered full sized guitars due to the length of the neck. A small child would benefit more from a scaled down guitar rather than a shorter length guitar.
A 1/2 size guitar will have a neck that is 1/2 the size of a full size guitar.
The main factor to consider when choosing a guitar is the height of the child.
If your child is near the next size up you may as well get the larger sized guitar considering kids grow quickly. I started a student 2 years ago who began when she was 7. She has a 1/2 size guitar. Today she must be almost 5 feet and the guitar seems really small for her. I may suggest soon that she get a larger guitar.
If you are ordering online you may want to go by the height chart, however if you have an opportunity to visit a store you may consider having your child try a few different guitars to see what they are most comfortable with. Unfortunately most of the guitar stores I've been to in Indianapolis don't stock many different scales of acoustic or electric guitars and the choices are pretty limited.
Guitars have different body sizes also. Some children who may be 11 and up or some women, particularly smaller women may want to choose a full sized guitar with a smaller body size or maybe even a 7/8 sized guitar. Dreadnought and jumbos are the largest body sized. Smaller body sizes are sometimes called parlor, folk or concert.
When choosing a size it is really the choice of the student and what they feel comfortable playing. I had a student female student who was about 5' 5". She began with a full sized Fender Stratocaster and later bought a full sized jumbo guitar. She handled the jumbo perfectly well.