It's not about you having short fingers , every body gets your problem at the very beginning , say for about couple of months or a little more then you'll never remember how bad you were. ;)
When you practice always keep in mind that your fingers should be perpindicular on the string when fretting it (well, you may see everybody fretting with an angle, but you have to learn the rules before you learn to break them)... Usualy ,for a beginner to get his fretting hand in shape, you should practice scales a lot ,then try slowly getting into simple chords.
It would be nice if you have a guitar teacher or a somehow experienced guitarist friend to help throughout your first few months with the guitar, then you can make progress on your own from books/vids/tabs/etc.