Deep sympathy. Yup, sleep was always a problem - not for DS, actually, but for me. For him there were different phases; up to about 6 months he didn't nap much [we took part in a study that involved recording minute by minute what he was doing for a day, several times, when he was a baby, so I have documentary evidence of this: at 6 weeks, he slept 10 hours in 24, total]. Then he did get into a nap habit, but his nighttime sleep fell apart and he started waking every hour at night. (So do appreciate your 1am to 9am-10am stretch, anyway - I'd have been
so jealous of that, any time in DS's first two years!)
Where you have a problem we didn't have is in that you say your DD actually seems tired and is fighting sleep, so our solution - observe that the baby is fine, focus on mum getting some sleep somehow, and say This Too Shall Pass - won't be adequate for you. Hmm...
I don't know a magic solution, but one thing I wonder is, how much are you and she getting out into daylight during the day? The study DS and I were part of was looking at the effects of sunlight on sleep (he also had to wear a light monitor) and I believe - yes, there's still a news item
here - that they found there was a connection. Now, they were looking at newborns, so it could be completely irrelevant for a baby of your DD's age, but if you have scope for getting out more in the 12pm - 4pm band, you never know, it might help. If you can do so in such a way that she gets a chance to explore and use some energy at the same time, that might give it another chance to work.
Good luck, and sympathy again: the lack of sleep was by a long way my least favourite thing about parenting a baby.
[ETA I second the recommendation for No Cry Sleep Solution, but the title oversells it IME ;-) ]
