Are there daycares that do one week on one week off?

Where are you located? And I would def check with the daycare. Some daycares do require a minimum per week and do part-time. I would talk to the other parent as and see how it can work out for daycare and if they can drop off your daughter as well while they have her.

Call the location you're interested in. They may be willing to do a custom arrangement.

Not many would accommodate that, but it’s always worth asking. Our nursery would do it, they’re very very flexible unlike all the others in my area.
Potentially a childminder might be more flexible