If she's not getting the calories she needs during the day, she will try to make up for it at night. If she is just nursing a bit to get back to sleep at night, then she doesn't need it. but if she is nursing af ull feed THEN going back to sleep, she may need it. However at 11 months old, she should only need one feeding a night, or none at all.
Cut out the earliest one. You didn't say when she wakes, but 6hrs sleep stretch is the 'norm' for an 11 month old. If she goes to bed at 9pm, that would put her at 3-4am for a feeding, and then be ok until morning.
Cut out the earliest feeding first, and employ your husbands help. Have HIM go in and comfort her without picking her up. It'll take a fwe days but if you don't go in, she'll relize she's ok and will fall back asleep. And you might even find if she sleeps through that nursing, she wil lstart sleeping all night, which is why its easier to tackle one at a time.
Also, its very common for babies to be distractable at this age. Much harder out in public since your baby likes to do the neck turn and either pull your nipple along or expose your boob! At home nurse her in one spot only all the time, like the rocking chairi n the nursery, or the recliner in the living room, etc. Pick a spot and that is your nursing spot, you two only sit there to nurse. TI'll make it more of a routine for her, lets go to the nrusing chair type of thing.