Is there any way you could move/rent by October, with a view to buying later? It would give her a chance to get settled in a primary school that would feed in to the secondary as well. The city schools are generally oversubscribed, except for North cambridge academy. Historically, it was considered a very poor choice, and still suffers from that reputation, although apparently has improved greatly from those days. But it is still not the first choice of many people.
Do you know where you are likely to be living? St Bede's has people coming from a much wider area, and as a result, has some buses as transport options. The others are likely to have people from relatively nearby, so it would make life easier for your DD if you lived in the area for her to meet friends etc. If you are likely to be living in a village becasue of house prices, as a lot of people have to do, better to know that now and apply to the nearby school. Traffic is really congested in the mornings and ideally you'll want to know how you plan for her to get to school before you choose one. In the city itself, many children will cycle.
Otherwise, wait and see what you get allocated as a late applicant next summer, get on the waiting list for whatever schools are nearer where you live, and prepare to travel a longish time in the morning to get to the allocated school for as long as it takes. It might not take long. I know people who have got into the most desired schools like Parkside over the summer, even from a distance, because others have moved or been settled at their allocated schools.
or you could appeal, if there are specific things that your DD needs that some schools offer. Some of them are quite different to others in terms of what languages, how much science, whether they set for subjects, what kind/how much music is available, sports, etc. so you might be able to come up with enough good reasons that she needs to go to your chosen school.
Chesterton is one of the bigger popular central schools. Parkside also seen as quite desirable but pretty tiny, so probably harder to get a waiting list place. Outside the city - Impington, Comberton, Swavesy, Sawston all possible choices, some quite big. Very different sides of the city though, so you really want to know whether you want to access north/south Cambridge to determine where you'll live first.