Kudos for nursing this long :) "Why do I want to wean?" That's the biggest question you need to ask yourself, along with "Do I really want to wean?" If you want to wean because everyone's telling you to, then IMO, that's not a good reason to take something away from your baby that she obviously still needs and very greatly wants. It's not ridiculous that she wants to nurse all night long; it's what babies/toddlers do. They're born with an innate need to suck and need to almost constantly. Even my 4yo son (who weaned at 2 1/2) sucks on his fingers, and I feel like it's a constant battle, but I also recognize that he's a kid, and kids are very oral. Have you considered a pacifier? Is she teething? That's prime molar age... :(
The first suggestion to you would be to try to get your daughter to start napping in her crib (if she doesn't already). When I was ready for my kids to be out of my bed, I started napping during the day in the crib, so they could get used to it. Once they napped fairly well, I would put them to bed at night (after nursing) in the crib. Both my babies were very different sleepers, so this process took different amounts of time, but I have to say that my 4yo sleeps with Daddy every night that he can while my 15mo daughter is perfectly happy in her crib for naps and the first part of the night.
When she wakes to eat (and she still does once each night), I nurse her lying down in my bed, so that we can both fall asleep if I choose to. More often than not, I put her back in her bed, then go back to sleep in my bed. I would just let her stay with me, but I'm a very light sleeper and don't get the sleep I need with someone else in bed with me. Yes, I nurse my 15mo once during the night, sometimes twice. Yes, she's genuinely hungry, as she gulps for 5-8 minutes before slowing down to comfort-suck and fall asleep. I don't say that to criticize or mock; I say that for your benefit, so you can feel like your 16mo nursing through the night is NORMAL :) Adults don't generally go 12-14 hours without eating, so why should we expect a 16mo to?
As far as her getting no milk, you'd be surprised how much milk your daughter is still getting. Believe it or not, you're probably producing almost as much as you did when she was 9mo; it's just in different quantities because your daughter nurses less often :)
I agree with Pamela that you should relax a little, but if you need to wean to do that, that's ok, too. Weaning in your house probably needs to start with the nights, especially since you didn't mention how often she nurses during the day. A friend of mine's son just night-weaned at 18mo, and she told him that the milk goes night-night, but it'll be awake when it's light out. She said he's doing surprisingly well, but I don't think I would try this kind of logic with her right away, cold turkey. Just some ideas, but try not to do a sudden weaning, as it could lead to all the problems we all try to avoid throughout nursing: plugged ducts, engorgement, etc. Good luck :)