Have you checked the admissions criteria for that particular school? Some schools state that children currently attending x infant school get priority over children attending y, even if they are not linked.
This isn't always the case though.
I would imagine that most parents in your area would be applying for the Junior School nearest to or linked to their infant school and they are likely to have the same amount of places in their intake so it is likely she would get a place.
It wouldn't harm to put a covering letter in. They can take into account the specific needs of your child (emotional/health etc) when allocating places.