Hi,
Since your child is one and a half years old, her food and nutritional requirement would have not been possible even if you had been having enough milk. Yes, feeding her off and on, or during night, not primarily to feed her but because kids are used to of latching and it is hard for them to wean is fine. I think you need to feed her properly before you put her to bed. After her meal, after a while, you can even make her drink milk. Only that, if the baby sleeps after having milk then you will have to make sure that you get up at night to make her pee, if you are reinforcing the habit of peeing in the toilet.
I think she is not eating properly or must be having her meal way too early and which is why she feels hungry at night. I think the best is let her have her dinner around 9 and then at around 10, make her drink milk. Or plus minus the timings according to her sleeping schedule. Then even if she will latch on to you, it will be just to get the feeling of being latched and not out of hunger.
Sometimes, babies internal clock is set to wake up at the same time as they do everyday. And at times, they wake up because of Startle Reflex, where the baby suddenly moves or stretches his arms or legs. This happens for just a few seconds but it wakes the baby up. And sometimes it also happens because if you say feed your baby in the afternoon four times or after 3 hours of interval then the same pattern is followed by the baby during the night.
All, I suggest for now is try feeding your baby well and feed her milk before she is about to sleep. This will keep her full throughout the night and she would sleep well. If this doesn't work, please see her paediatrician and take his advice.