I think some kind of plan at the moment is a good idea, even if her abilities do change later on - at the moment, she is well ahead of the others, and that needs dealing with in a suitable way.
I wouldn't be surprised if socially she isn't great, because in many ways, it's hard to socialise with children who don't have similar interests. I was reading far beyond the level of others in my year, and for quite a while, just had interests that were different as well. It doesn't necessarily mean social skills are poor, but that there may be few others that she really has a connection with. So encouraging friendships with other ages is fine, or even not worrying if she doesn't seem to have friends her age but prefers to read or spend time alone - it's not always because a child can't make friends, but just that they are actually quite different. Other activities with children who are also passionate about something particular - e.g., music or chess or whatever - might give opportunities.
I'd also be a bit wary of making her help others too much. yes, a little of this can be good at developing compassion and understanding, and yes, there are some things that a bright child can gain in terms of their own levels by explaining to others, but when there is that much of a gap, it doesn't really help the child who is tutoring understand the work any better themselves, because they really don't need that. In my case, it ended up just hampering socially, because the other children didn't see me as a peer, exactly, but more like an older child, older sibling etc, someone that they come for help to rather than someone that they'd just be friends with. It was also clear that boys who were well ahead didn't get used in this way as much as girls did, but were challenged more, especially in maths.
Another difficulty is that if a child isn't stretched in a good way, they might end up challenging themselves in ways that are not that helpful - in my case, perfectionism. Aiming for perfect scores on things gave me something to work for and achieve, but ultimately didn't help me learn to cope with mistakes or failure very well, and gave far too much importance to perfection. Learning to accept something that was 'almost perfect' and then sometimes moving on to something that was actually a bit of a challenge intellectually would probably have been better for me. You don't always want this - there is some benefit in being able to strive for perfection, and to enjoy the achievement of 'getting there' and being able to do something easily and well, rather than just always having more challenges put in front of you, which can at times also destroy motivation. But there's a balance to be had.
Things that would have helped - simply reading was a huge one; you can learn so much from both fiction and non-fiction, and having a bit of directed work this way, advice/discussions etc would have kept me very occupied. Maths challenges - not left to my own devices, but actually shown how to approach things, problem solving methods, ideas, etc. Learning associated skills like computer programming. Working on other activities like music or crafts or whatever - again being taught properly, not just told to do it to fill in time on my own. Puzzles - word puzzles, logic puzzles etc.