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I play accoustic guitar, mostly folk music and have small hands and I am small in stature, so I am recommending two guitars that I am familiar with, that work for me with enabling me to play without stretching to reach a cord.
A Taylor Baby Taylor Deadnought Acoustic Guitar is made for a smaller person, so they are a small guitar and has a smaller fretboard for a smaller hand. They are a high quality but not overly priced. This is a link to view it: http://www.guitarcenter.com/Taylor-Baby-Taylor-Dreadnought-Acoustic-Guitar-100447175-i1148421.gc?CJAID=10449560&CJPID=1759905
The Martin LX1 is also a good 3/4 acustic guitar. Again it is made for the smaller hand and a good beginner Guitar: http://www.guitarcenter.com/Martin-LX1-Little-Martin-Acoustic-Guitar-102969268-i1148317.gc?CJAID=10449560&CJPID=1759905
I have very small hands as I wear a size 4 ring and cannot span the fret board or neck on a full size acoustic guitar. I have tried both of these and have found I can span the fret board to make sure I can play cords comfortably and am able to finger pick and play without major issues. Both of these guitars have a good tone and would make a good starter guitar for someone who is just getting started.
I do suggest getting into a Music shop if possible and hold some of the guitars to get the feel of the neck and fret board and ask about the two guitars I mentioned above and see if they have one for you to try. Joan