It's hard, isn't it? If your daughter is thrilled with her friends and you don't think she'll get that with home education, I can see why you'd hesitate to take her out of school... especially if it is you and not she who is dissatisfied with her education.
Are there many home educated kids where you live, do you know? In my area, there is scope for kids to see specific HE friends maybe three times a week just by going along to home ed groups, even where parents don't bother to arrange playdates. With playdates, my older daughter used to see her closest friend for an average of about 2.5 entire days a week. That's 2.5 full days of nonstop playing, not just the breaktimes and brief conversations snatched in class before being brought back "on task" by a teacher. That wasn't effortless though: I was forever driving back and forth! I jokingly grumble to her that she is only allowed to make friends with kids in our neighbourhood, but she constantly disobeys me about that and gives me the Bambi eyes about taking her to see far-flung friends.
It's worth considering that a small close friendship group which is together five days a week is wonderful right now but can be a mixed blessing in the long term. No doubt you've heard the parents of older children (often girls) mention the pain when one of the other kids in that group decides it's time for one of them to get pushed out. There your daughter is, in the same room with those kids day after day while they give her the cold shoulder. Or maybe she's one of the perpetrators, colluding in excluding somebody else because she knows if she doesn't go along with it, the others could turn on her. At school, unlike most other social settings, there is no escape when things go pear-shaped. Interactions are in a public spotlight.
By contrast, when my dd's former best friend began saying unpleasant things about her behind her back, she was able to avoid her most of the time and fairly easily shifted her attention over to other friends. The betrayal still hurt, but she had more options in addressing it. Just think, wouldn't it be rather horrible if your partner's affections were transferred from you onto your best friend and you had to carry on sharing a house with both of them? That's how it is when kids at school fall out with close friends. We expect them to just be brave and move on, but that's hard when they are stuck in the same place.
A wide friendship circle, with different kids seen in different settings, can be very healthy. That isn't just because it can avoid the potential problem I described above. It's also because it allows children to experience a whole variety of different roles. My younger child, for example, goes to a couple of HE groups in which she's the oldest. She loves to be the competent and helpful one for a change, the leader, the admired and sought-after. In other settings she is one of the youngest, and she in turn is the one who is nurtured and helped. Then there's my 15yo daughter, who may play sports with and seek careers advice from adults on Sunday, go shopping with teenaged girls Monday, spend the day in solitude on Tuesday, and go round to play Minecraft with a ten year old boy Wednesday. That isn't much seen at school; I remember when I was at school it was frowned on even to have a friend in the year below, let alone a boy - not that there would even be much opportunity to develop such a friendship in such a strictly age-segregated environment.
It would be hard to take your daughter away from her friends if she is happy at school. On the other hand, you can't predict how rich her social life outside of school may be. It's a gamble, just like moving house. Not much help, am I?