First, your daughter is nursing in the middle of the night because she is hungry. At 6 months she can eat a breakfast of cereal and a baby food jar of fruit, lunch with a different kind of cereal and a baby food vegetable, and dinner with a different kind of cereal and a baby food vegetable and a baby food fruit. If she is not on three meals a day gradually introduce those meals. Feed her the breakfast and dinner at home so that you know she is getting enough to eat at those two meals. Drop in at the daycare at lunch time and see what they are feeding her. If your job is such that you cannot leave work then ask the daycare to report to you how much she eats for lunch every day. You can also give her a snack before bedtime. My kids loved yogurt for a snack. We gave them plain yogurt when they were babies. The first thing I did when I walked in the door after work was nurse the baby. Then I cooked dinner and fed the baby while we ate dinner. After dinner I would give the baby a bath and then nurse the baby to sleep.
Second, you are putting her to bed too early. Try 15-20 minutes later per night and get her to an 8:30 or 9:00 bedtime. Nurse her well before she goes to sleep. If you are tired at the end of the day then your milk supply will be lower. Drink a huge glass of juice or water when you walk in the door from work. Eat a healthy dinner. Pump after she nurses to increase your milk supply.
Third, she may be nursing more frequently because your milk supply is low. Make sure you are getting enough rest, eating nutritious meals, and drinking plenty of fluids. If your milk supply is low she will nurse more frequently. Take a case of bottled water with you to work and make yourself drink more fluids during the day. Don't skip lunch. Eat lunch every day. Nursing moms need to go to bed earlier than you normally do. Try going to bed 30 minutes to an hour earlier than you normally do. You will be surprised how much that extra 30 minutes or an hour of sleep helps.
Fourth, if your husband is not helping around the house he needs to start. If you cook dinner he needs to do the dishes. While you nurse the baby to sleep he needs to pick up the house and put in a load of laundry. Just those little things will help you get to bed earlier and get the rest you need as a nursing working mommy.
Fifth, the only way to get any sleep as a nursing working mom is to put the baby in bed with you in the middle of the night to nurse her. My babies would nurse on one side and make little noises and wake me up and I would put them over my stomach to burp. I would switch them to the other side and they would nurse and fall asleep. I would usually wake back up when they fell asleep and nudge my husband and he would put the baby back in the crib.
Now, you are not going to want to hear this, but, my oldest son nursed twice in the middle of the night until he was a year old and he nursed once in the middle of the night until he was 18 months old. He was a hungry baby. He was off the growth chart for height and weight until he was in school and then he was at the 90th percentile. He is 18 years old now and he still eats all the time. He is 6'0" tall and weighs 215 pounds. He plays 4 sports and needs a lot of food for fuel to do that. Some kids just need more to eat and it started when he was a baby. He still gets up some nights in the middle of the night and gets something to eat or a glass of milk. He is just a hungry kid.
Last thing, nap on the weekends during the day when the baby naps. You cannot believe how much a little nap on the weekends will help!
Enjoy your baby!