Bute House is a lottery so you are not too late. Depending on what kindof school you like, arguably best school for girls in west london.
Falkner House, Queens Gate, Ken Prep are all assessments so you have plenty of time
Thomas' is an assessment but only if you register early enough, from my experience you are too late for them.
Pembridge, Norland, Orchard House, Ravenscourt Pak prep you are all officially too late for. However Pembridge has had a lot of churn. We were on the wait list from when DD was born until June this year (she starts in Sept) when we got offered a place. They had been so curt with us in the process that I turned them down (we have another place we are happy about). However when a friend went round to visit (you don't have to pay to visit, you do have to pay to register. You are not invited to visit until you are offered a place, though, and you'd have to pay first term's fees to accept the offer, usually within a week, so that's not far off). So if you are keen on Pembridge it would be fine to put her down now.
But your issue is you are not going to know about either the assessment schools or the 'put them down at birth' schools for another 2-4 years, so think it's a bit odd to decide where to live based on this. Why not look for where you'd like to live (sounds like notting hilly area) and then put her down for all the sensible schools, and see what happens. My strong guess is that she will get in somewhere, although it may go down to the wire.
If you want north west london btw, you've got all the hampstead schools - north bridge house, devonshire house etc. Think you should just go for it!