Leslie,
Sorry I am jumping in here a bit late but I wanted to tell you I can really relate to your DD's sleeping issues.
Zoey started taking 40 minute naps at 2 months and continued on with this her whole life. I was SO frustrated for SO long and tried everything under the sun to extend her naps, etc. It became really consuming and I really felt frustrated, and even resorted to holding her during naps to ensure she slept well. Of course, I had no life because of this and was miserable!!! Eventually, I just accepted the fact that my daughter did not need a lot of daytime sleep and life became much less stressful. At 12 months Zoey was taking two 40 minute naps per day and sleeping around 11-12 hours at night. At that point, she started daycare and by 13 months the DCP had her taking only one nap. At daycare, this nap is normally at least 1.5 hours. She usually sleeps 12 hours exactly at night.
At home on the weekends she often will only have one 40 minute nap, but mostly it is about 1 hour. Often with me she wakes up VERY grumpy from her nap because she's not slept enough. On those days I put Zoey down 20-30 minutes early for bed. If she seems super tired early in the day, I sometimes just give her two naps, knowing they will both be short. A few times over the holidays I put her down for what I thought was a morning nap and she slept for 2.5 hours (we had a few late nights over the holidays and she was OT)! She seems to be able to let me know when she is more tired by her moods and I just try to go with it.
Zoey is 15 months now and her day is something like this....
She wakes around 7:15-7:30, has lunch at 11am and is in bed for her nap by 12. At daycare she sleeps until 1:30. We have dinner at 6:30pm or so and she is in bed asleep by 7:30pm. On weekends, if she has a short nap I often put her to bed by 7-7:15pm and this seems to nip any early wakings or bad night sleeps in the bud.
I always make sure Zoey has a full tummy before nap and bedtime, has had a poop (she poops a lot), has had plenty to drink, and is not too hot/cold. That way, I am ruling out any of these things from being the cause of her waking too early. If I suspect she is teething, I give her some infant Tylenol about 30 minutes before her nap.
Anyway, just wanted to let you know you are not alone with having a short napper and I hope you are able to get into some sort of routine with her.