I hate to put a dampner on anyone's hopes but would also hate to give false ones.
In assuming that a certain percentage of children who have attained a higher score will in fact be given a school that is a higher choice, I am afraid it is not quite as simple as the formula that has been suggested.
A very significant percentage of children in the top 100 or top 150 may have also attained the mark for another Grammar - perhaps a KE Grammar closer to their home - but this is less likely to be the case for children lower down in scoring. They are more likely to need and take the QM place in all honesty.
However, your daughter was ranked 294. Last year, the final candidate to be offered a place was 268 (although this was higher in previous years and could possibly be higher again this year). There is a difference of 16 pupils between this score and your daughter's score. However, an extra 16 places have been added this year. You can therefore assume that if everything stays exactly the same, your daughter will manage to obtain a place. However, it doesn't always stay the same, I am afraid, particularly as, due to the recession, more parents seem to be choosing Grammar over Independent and this will increase the number of the 'last rank in', not decrease it.
Your daughter's score is borderline - certainly enough to be worth putting the school as first choice if it is your first choice, but not enough, sadly for you, to know for sure that a place will be forthcoming.
If, on 1 March, your daughter does not have a place at QMH, she will automatically be placed on the waiting list based on her score - unless she received a place at a school which you ranked higher on your form, in which case she obviously won't receive a waiting list place.
For example in ds1's year, I was aware of a girl who had Alderbrook (comprehensive) as first choice and CHG as second choice. Despite (from what I was told) gaining a high enough score for CHG she was offered her first choice, Alderbrook, as this was her catchment school and she had a certain chance of entry. She had no 'right of appeal' as she was offered her first choice school on her form.
This is why it is important to put schools in your genuine order of preference. They do not know which order you have placed them in and it will not effect her chances of places in other schools, such as comprehensives, if QMH was placed first.
You can actually join waiting lists later, but processing this could take around 3 weeks in Birmingham anyway (Walsall may be faster) so you could miss out on precious opportunities to be offered a place in that time. Better to have it as a first or high preference on your form so she automatically joins the waiting list on 1 March - if not offered a place then.
The waiting list usually moves quite a lot around 16 March (not that exact date but around that time) when the final day for accepting school places arrives.
This is when, in the past, I know that parents have received calls offering their children places from the waiting list. However the lists continue to move a little all the way to September, as perhaps children move away, change their mind, receive a higher preference, etc.
If you want a child to remain on the waiting list once the Autumn terms begins, you need to inform your LA and/or school.
One year, on the first day at CHB, a boy didn't arrive, and so when the Head found out that he had relocated without informing the school, he called the first boy on the waiting list. His parents took the call, went to collect the boy from his new school, stopped at the shop to kit him with new uniform, and had him at CHB before the afternoon. While I do hope you don't have to 'sail so close to the wire' - it shows that children do attain places from the waiting list!