Just a warning that you may not necessarily just get your daughter into a good Primary in Birmingham just because you have moved nearby- they are massively oversubscribed, many already with classes of over 30. There are however excellent schools in Solihull and Sutton Coldfield that may well have places.
I know myself from having enquired, that there are huge waiting lists at the good primaries in Kings Heath and you may well be allocated one that is not so good at all. If you are Catholic (St Dunstan's) or C of E (Moseley) you may be in with more of a chance. I have to apply for ds3's Primary place now and was told that last year, the cut off for Colmore was 0.4 miles
Not trying to put you off - just thought I would mention it.
My son says that a boy in his year at CH comes from somewhere round Derbyshire - he commutes in with his Dad, who works in Brum. Another lives in Wolverhampton, also with a dad who works in Brum. But I do feel that they must struggle with the commute. One parent in Sutton Coldfield said her son gets home about 5.30pm from the Green bus. My own son gets home about 4.15pm - which gives him a full hour and 15 minutes extra for homework - it really is a lot easier if you don't have a massive commute.