At 9 months, you could offer water. After a few nights, they stop waking. The waking is a habit, more than a need. So you offer water, she cries, you hold her, but don't offer your boob! Just keep on holding her till she calms down, and then put her to sleep the way you do at the start of the night. If you are nursing her to sleep, then you need to stop doing this. You need to stop nursing her when she is merely drowsy, and then put her down.
If you want to CIO, then don't pick her up, pat her back, tell her it's night, night time, go back to sleep, and then leave the room. She will scream, let her scream for 5 minutes, then go in again and do it, then wait 10, then on the 15, I always say," I'm not coming back in here." She will scream, maybe for an hour till she puts herself back to bed. She will scream the next night too, but by night 3, she should cry a lot less, and by night 5 she will be able to put herself back to sleep.
It's hard, truly gut retching to hear a baby scream, but sometimes it's better for the whole family if everyone gets some sleep. You sound done with your current situation, so if offering water instead of milk doesn't work, it might be time to sleep train. If you don't want to CIO, get the No Cry Sleep Solution. If you want to offer water, I'd night wean first. So nurse for 1 minutes less every other day. When you get down to 2 minutes, baby shouldn't wake. If she does, she only gets water.
They wake out of habit. It's now her habit for you to put her back to sleep, so you need to break that habit. 9 months is plenty old enough to put themselves to sleep. It takes some work on your part, but it is possible. Check out the No Cry Sleep Solution, but if you want immediate changes, you may need to CIO. I found Pantly's method to take 3 months with my daughter. It was awful. One other good book that I used with my son was the Baby Whisperer. She doesn't believe in full blown CIO, instead, you hold the baby while they scream. I have no idea what her solutions are for 9 months, as I used her method with my son at 6.
But the water might actually work for you at 9 months. So start night weaning, and then when you get down to a few minutes, if she still wakes, offer water.
Also, I think you are in a wonder period, so most 9months old wake and stay awake for periods of time at this age.