I would take whatever is the lightest and most compact. If you are going out a lot, there are nice children's bags but they cost about $100. I got my grandson one last year. For once in a while outings, nothing wrong with your idea of using an adult bag and just tying the foot so it fits. Just have your daughter wear some warm clothes and a hat to bed.

Some UL adult bags are a bit fragile, so if your daughter is gentle on gear, OK, but if rough then I would hesitate. (I know my grandsons would start a sleeping bag fight in minute! stomp on the bag, wrestle and all those other things 8-year old boys do).