My (now 6 year old) daughter was very much like yours. She didn't want to sleep in her crib at night, she didn't sleep much during the day either, and I was EXHAUSTED! Now that I've had 2 children, I can look back with 20/20 hindsight and see some of the mistakes I made that made sleeping hard for my daughter and I. I hope it will help, even if your situation might be a little different.
I also nursed both my babies and loved it. Nursing at night made it easier to sleep for both baby and I, and often the kiddos would nurse themselves to sleep and I would leave them in bed with me. Althought that was great when my kids were younger than 3 months, once they got to be 5 and 6 months old, they became convinced that they could only fall asleep by nursing. This started a vicious cycle, wherein baby would wake up every hour to nurse, not because they were hungry but because I was close and it was comforting. When my daughter was almost 9 months old, she woke up one night at 12am and stayed awake until 5:30 am playing. I sat on the couch watching her play and crying because I was beyond exhausted at that point. It suddenly occurred to me that I did not need to be sitting there, she was the baby and I was the mom. So, I put her in her crib and listed to her scream at the top of her lungs for 2 HOURS! She did finally fall asleep, but it was torture for me to listen to it. When she woke up, though, it was like it never happened. She was her usual happy self. She, like your daughter, was horrified at being put into her crib. She would work herself into a frenzy if we put her to bed awake. The best advice I can give you is to start now by putting her to bed awake when it is bedtime. Set a bedtime and stick to it. At her age, she's old enough to cry for a little while, it really won't hurt her. My rule of thumb was to not let them cry for more than 15 minutes. If they were still crying after 15 minutes, I would go in and rub their back, but I didn't pick them up. The next time I would wait 20 minutes before I went back and so on. Within a week, both of my kids got into a very health and much needed sleeping schedule.
I do think there are some babies that do not sleep as much as others, and it seems perfectly normal and healthy. My daughter at 6 months old only took one nap a day, and she also never seemed tired, even when she should have been. Here is a clue to watch for that I figured out from my little girl. She actually got more active as she got more tired. It was almost as though when her body got tired, she started working harder to stay awake. Once I cued into that, it was much easier to tell when she was sleepy. She didn't have the normal tired baby signs like rubbing her eyes or yawning, she just got hyper! LOL
Since I learned from my first baby, my second baby's sleep schedule was so much easier. I wish you the best of luck!