Cathy,
It sounds like your daughter is making wonderful progress in growing in maturity and independence. It is such a blessing to train our children in this needed skill in bite-sized steps rather than waiting to thrust it upon them once they reach high school!

We have found that our children take much care and are proud of their work that they do independently.

They have taken hold of so many skills in this way that otherwise would have been mom-enforced.
My two oldest sons both realized on their own that they could set their alarms and get up at 6:00 (by their own choice) in order to get started on their independent subjects when the house is quiet. This helps them be done earlier during the day with their schoolwork.

I set their start time later than 6:00, but they have continued to choose to get up early this whole schoolyear as they are motivated by what they are able to complete on their own.

If I was still the one doing all of the reading to them, and they were still tied to the rest of the younger kiddos for many of their subjects this wouldn't have happened. As then they would be waiting on me to "provide" their education, rather than self-starting. So, we've found wonderful motivation and enthusiasm from our boys with their increasing independence. Yet, our family is together for so much of the day that we don't miss out on our family time either. For us, if our kiddos weren't working toward independence, there would be no personal time focused just on each child and his/her education.
As far as independence goes, from my perspective, I do still check everything my kiddos do, even the 'I' boxes. I sit with my second son in late morning and I skim over each of his boxes in his guide while checking the product to make sure he's accomplished everything needed. I often read a couple key ideas aloud to him from several of the boxes and go over a few things that may have had questions just to be sure he's done. I have my son sit with me during this time, as I check everything and have him put it away after I check each item. This way we can discuss very briefly as I quickly look his work over. It takes about 15-20 extra minutes, and we call this our meeting time.
For my oldest son, I check all of his work at lunchtime while he's eating and go over any needed fixes after lunch. This works well for him.
With my youngers, I am with them for all subjects and just check each one as we go.
Blessings,
Carrie