PDog, sorry to hear things are rubbish - and sorry for appearing to ignore your post yesterday: I didn't see it when I put my last one up.
IC, I've never been able to work out why hugs are unmumsnetty (although I know they are!). Can you enlighten me?
Kaymer, from the fact that your DD used to be able to feed to sleep and sleep longer, in theory (ha!) she should be able to do it again. I'm guessing that the needing to suck-to-sleep association is likely your problem, as it was my DS's.
Your naps sound good so I doubt that chronic overtiredness is a problem. I find the link between day and night sleep is that general overtiredness = generally frequent waking, rather than one day necessarily affecting the following night.
Getting her to self-settle at bedtime would probably help (although she might still wake) but if she's a tension increaser, it will probably involve a fair bit of crying. (See here on how to work out if she's an increaser or releaser).
I'd try to introduce some sleep cues to use alongside a different method of getting her to sleep. I sing a song, but you can use words or even a CD. Pick one you are happy to hear over and over again! Sing it when she's dropping off to sleep (I did this during naps). After 4 days or so she should associate it with feeling drowsy.
You could do the same with something like patting. It might be hard to do while she's feeding to sleep, but you could try patting her for a minute after she's unlatched. Then she'll associate the feeling with being relaxed and sleepy / asleep.
The Pantley Pull-Off technique here from the No-Cry Sleep Solution is worth a try, although it takes a while. I'd use this at the same time as singing the song or whatever. The idea is that when the LO finally drops off, your nipple isn't in their mouth.
By the time I'd finished doing all of this, DS still needed at least one night feed, but he'd feed, unlatch himself, roll over and go off. I was amazed - it was just like Elizabeth Pantley described.
I reckon that if you're there, she won't be fobbed off with a feed so you'll probably need to get your DH to help. (I'm lucky in that DS will settle for me without feeding). Perhaps you could camp out on the sofa for a few nights?
Your DH can then try to get her back to sleep without being fed. Rocking or frantic jiggling / bouncing works for my DS. Sometimes he needs to be patted assertively on the back at the same time. This is the time to use your music cue to help her feel drowsy.
If after 15 mins she's not showing any sign of going to sleep, give up and feed, then try again either the next waking or the next day.
When I started doing this, I could sometimes pat DS back to sleep without picking him up - but only if I got to him the moment he woke. His first waking is always 45 mins after bedtime so I'd lurk there ready to pat him at the first sniff. Now I need to pick him up & rock him but again, it's easiest to get him back off if he's not had chance to really wake up properly.
The problem I then had was that I couldn't put him down without him waking and crying. That was when I did PUPD. So it'd go DS wakes - pick up - rock to sleep - put down - cry - pick up - rock to sleep - put down - cry - pick up etc.
I'm not sure that's how PUPD is 'officially' supposed to work, but it worked for me. At first it took over 20 mins to be able to put him down, but eventually I was just picking him up once. As he got more used to it, I could just rock him till he stopped crying rather than rock him till he was completely asleep.
When I did put him down, I'd pat him and keep singing the sleepy music, which helped.
Doing this every time she wakes would probably be a big job for your DH if he's not used to getting up at night. He could try doing it for the evening wakings first and then go back to feeding after you go to bed. That's likely to take longer to have an effect, though.
I think that needing help to go to sleep is more of an issue than feeding to sleep itself. So at the moment, I feed DS to sleep at bedtime, then he wakes after every sleep cycle during the evening. When that happens, I rock him to sleep but it doesn't stop him waking next time. The PUPD bit seemed to make the crucial difference.
You may find that it doesn't work - 9 months is a difficult time with the developmental spurts going on at around 37 and 46 weeks. If it doesn't work, don't despair and try again a week or two later when your DD may find it easier to settle.
I'm aiming to try all of the above again in a few weeks' time once we're well clear of the next developmental spurt. Can't wait! 
Shout if any of that doesn't make sense.
Good luck, whatever you decide to do. :)