You can absolutely do this. However, choosing seats at check-in really makes it quite unlikely that you'll get to sit together.
The way to play it safe is to pay for seat reservations at the time of booking and book seats side-by-side so that you are together. Availability should be good if you do this when you book the ticket.
You can certainly do it the way you've outlined, but there's a high probability you won't get to sit together, and while the airline can ask people to move, because your daughter is not that young, passengers will be under no obligation to move for her. (In fact, if they paid for their own seat reservation, they might resent being asked.)
Pay for seats at booking, and your problem is solved.
One other option: you can book this as two one-way flights. Book a one-way flight to the destination, with both of you as passengers, and then a one-way flight home for just her. You still run into some risk of not getting seated together if you don't pay the seat fee, but the risk is smaller since you'll be physically checking in simultaneously. (It will still be based on availability of course. If all that are left are middle seats, you're both going to be in middle seats, and not together.)