Sorry- if she enters Y4 in Sept, and moves to Birmingham 18mo later... she will be arriving halfway through Y5...
You need to consult prep schools now if you want her to have a place then- the good ones are oversubscribed I'm afraid. Try- Blue Coat, Hallfield, Norfolk House, Edgbaston Girls', Highclare (though this is north of the city, and the others are all Edgbaston). For state schools, you cannot apply for a place until she is living in the authority, and for in-year admissions you approach the school directly, though you can check with the LEA Admissions team whether or not there are any places at the schools you have chosen.
Which schools are your friends saying are so good?
The selective independents are in Edgbaston- King Edwards Girls', Edgbaston High School for Girls. There is also Solihull school, in Solihull, natch.
The grammar schools are- King Edward VI Camp Hill Girls', King Edward VI Handsworth Girls', King Edward VI Five Ways (mixed), Sutton Coldfield Girls'. There is information on all the schools in the King Edward Foundation (including independent) here. The grammar schools are indeed excellent schools, however I cannot emphasise enough just how fierce competition is for the places- there are only 120 places in each school each year- girls from all over the West Midlands apply, not just in Birmingham, and Birmingham LEA alone has 7000 girls in a year's cohort!
IMO there is no point in tutoring from Y3- if they need that much help then they are not going to cope with the standard expected at the secondary school anyway, however- she will have to have some preparation in examination technique otherwise no matter how bright she is she will founder. However, if she is in a Birmingham prep school, she will receive a little coaching in this prior to the examinations.
If there is any chance of DD2 going independent too, then you will need to get her on the waiting lists before you move to Birmingham- ie now.
If DD1 doesn't get a grammar/independent place, you will need to live in pretty close proximity to school to get a place at a good state secondary- the best ones would likely be- Arthur Terry and Plantsbrook (in Sutton Coldfield), Kings Norton Girls' in Cotteridge, Lordswood Girls' in Harborne maybe, erm.... thats about it IMO (sorry- hope I don't offend anyone with that viewpoint) unless you are catholic then you could add Bishop Challoner in Kings Heath and St Paul's Girls' in Ladywood.