Heels is right - if a school is over-subscribed, they have to make a selection somehow. The first-come-first-served, names-at-birth approach isn't fair as it biased against summer-borns. A lottery system might seem fair, but the school might end up with a class of personalities that don't mix well.
However (and I say this as a parents whose DCs have done 4+), I don't agree with basing assessments on "academic" skills such as reading and writing either. Precocity isn't a reliable marker of future academic success, and it seems wrong to brand 3-year-olds as failures simply because they aren't precocious.
OP, are you doomed? Not necessarily. I think it very much depends on which schools you are sitting for and what they are looking for at assessment.
DS1 sat 4+ at two schools, one of which is reasonably academic. One was a group assessment, and instead of lining up nicely with all the other children to go off to the classroom (minus parents), he flatly refused to go and had to be carried (by me) amid much protest to the door of the classroom and handed bodily to the teacher. He came out 45 minutes later beaming having had a great time. Assessment tasks were along the lines of problem-solving and group interaction, with a bit of counting and colour recognition thrown in, rather than testing lots of formal academics. Having read MN horror stories, I assumed he had blown it for refusing to leave me to go into the assessment. No - he was offered a place and several years later is thriving in what is definitely a good fit of school for him. I think the crucial thing was that the school were (and still are) very understanding of perfectly normal small child behaviour, and didn't penalise a 3-y-o for behaving like a 3-y-o.
The second assessment was an individual one. DS1 wanted to wear his favourite dress-up costume. I let him - thought the school might as well see the sort of child they would be getting. Assessment test were simple language and reasoning tasks with a bit of phonics and counting thrown in. Again he was offered a place.
We didn't do any preparation for the assessments other than taking DS to some free museum group activities for kids to familiarise him with the situation of answering questions and taking instructions from a strange adult and interacting with kids he didn't know. Certainly no tutoring, and his relaxed Montessori nursery didn't specifically prep for assessments afaik.
I think at some level you have to trust in your choice of schools, and that if the school is right for your DD then hopefully she'll get a place. Please don't tutor her. That's just buying into the madness - and how on earth do you explain it to the child without them becoming aware that they are going to attend an assessment? Neither of mine had any idea they were being assessed - as far as they were concerned they were just going to play at big school to see what it was like.
I wish your DD the best of luck withe assessments (and you too - it is far more stressful for the parents than the children, believe me!).