11mo sleeps like a newborn!

My almost 11 month old daughter wakes up constantly at night. She's up every 2-4 hours, but 4 hour stretches are rare. She's been doing this since about 6 months old. I am exhausted and am going back to work soon. I'm desperate for more sleep! She wants to nurse every time she's up, and because she's small, our Dr said to nurse any time she wants to. I can tell the difference. Sometimes she wakes up and cuddles for a few minutes then I put her back down and she sleeps, but other times I pick her up and she starts rooting or sucking on whatever exposed skin she can find. Our Dr recommended we give her a bit of formula at bedtime to keep her full longer, but my daughter has a dairy allergy and with the shortage we can't get the formula she needs. Any ideas??