It strikes me all the places she wants to go are very expensive when there, not just to get to, which is something to consider. Is she open to other destinations?
I'd recommend you sign up to Jack's Flight Club, they do impartial and reliable alerts on good flight deals and sales. It's usually about £50 a year but if you want to pm me I have a code to get it to £35 plus a free month. Be open on where you go rather than looking for a specific place if possible, so we've been to Vancouver for under £250 per person, South Africa for £350, Bali for £420 (thoroughly recommend Bali for both culture, friendliness, accessibility but also it's insanely cheap, you can get a very nice hotel there for under £30 a night and realistically about £10 a night in the city. You can hire a driver for the day for about £25, I had plenty of meals out for under £2), New York for £180, Iceland for £45, Ireland for £8, Barcelona for £18, Morocco for £42, Singapore for £410 etc. Once you have flights head to trivago to see what accomodation is about as it's a screenscraper for all the big booking sites and it is worth considering the cost once you're there (so Vancouver was a great deal on flights but Jesus it was expensive to stay there, whereas Bali was more on flights but I spent less than £150 a week on all excursions and food and went out and about every single day on that, so once the flights were paid I could stay there nearly two weeks for what one days hotel, food and transport cost in Canada). Consider what you actually need in accomodation, so if you're going somewhere new and cultured to explore and just need it as a base to lay your head it's pointless getting the all singing and all dancing complex when the clean and friendly but with fewer facilities place will do fine. I'd also consider signing up to the Travelzoo top 20 email, because they sometimes have some exceptional last minute package type deals but they're rarely in school holidays.
Our kids have done long and short haul holidays this way since toddlers, and while I appreciate some think it's a waste before teens I think they got a lot out of it, they remember things they saw at age 3 or 4 nearly a decade later, some experiences have given them a much greater appreciation of the inequalities in the world (when we were sent to the 'expensive hospital for white people' in south africa when we thought our son had a broken arm, we had an assigned nurse, all xrays done and given to us on a disk, painkillers, no wait, a consultant checked in 3 times in 4 hours, and at the end we were presented with a bill for under £100. My eldest had a lot of questions at the time aged 5, but then used that experience for a school assignment at 11 and got a writing award for it) and some just really meant something to them like seeing their favourite animals in the wild, trying a special new food or odd things like the time we stumbled on a classical concert on the water where all the audience were in canoes!
If you have some disposible income then it's possible to travel and get a lot out of it with your daughter if you can put the time into finding a deal.