V.G.
I hope this doesn't discourage you too much, but this sounds exactly like my sons. Neither of them seemed to require as much sleep as the books suggest or what my most of my friend's children seemed to need.
My suggestions - Don't worry that her naps are short. She will sleep as much as she needs to sleep.
Some things that might help to make sure she sleeps better at night -
Make sure she gets lots of exercise and fresh air. Take her for walk outside in a stroller or in a backpack in the late afternoon or early evening. (It's a great time of the year to walk around the neighborhood looking a Christmas lights and there's nothing like coming into a warm house after being outside in the cool air to make someone drowsy!)
Give her lots of playtime to crawl or roll around freely in the afternoon and evening and then give her a bath to enjoy some play time with water toys to help her relax. Try to make sure she is mentally and physically tired!
Try delaying her bed time until later to make sure she is tired enough to sleep soundly and avoid the 4am poopy diaper. (I didn't try to put mine to bed until around 8 or 9pm!) If she eats/nurses later and goes to bed later it may delay the dirty diaper to a later time that is more reasonable for her parents.
You are not alone - it seems like a lot of babies go through an adjustment in their sleep habits when they are about 6 to 8 months old.
I know parents who would put their kids in their carseat and drive around the block to put them to sleep. I tried that and it didn't work for me! They did fall asleep in the car, but they always seemed to wake up when I took them out of their car seat to put them in their bed.
Good luck!