I’m sorry to hear of your circumstance.
Could you suggest going to mediation? They are specialist in trying to organise an amicable arrangement to suit your daughters child care without you both having to go court, they will speak to you both seperatley first to desifer what your thoughts are regarding, it is worth trying to think ahead also ie. With regard to Christmas, birthdays after school arrangements, the more you can put on the table will save you later in the long run as you will have already made the arrangement when it comes to it later on along the line (years ahead) . If you can both agree to an arrangement you can then ask if there is a possibility to get it legally binding by a solicitor to ensure you both adhere to it and potentially saving you having to go to court or to be back to square one again.
If your work is flexible and you are compitant, there should be no reason you couldn’t have your daughter 50/50 for instance your ex has your daughter half the week and vice versa, first and foremost tho the consideration of your daughter needs to be paramount and whatever the arrangement must suit your daughters needs first and not to suit others and so not to disrupt her routine, so I would suggest also arranging suitable times for her to be picked up, dropped off and bedtime for you both to adhere to, again so your daughter is keeping to a structure with you both.
I hope you are able to come to an agreement.
Hope this helps!
Best wishes