"Gifted" is not the same as "academically advanced" though the two often go together. But really there is not usually any formal "gifted" designation until children are in about the second to third grade. All that aside, however, I would not focus too much right now on her giftedness; she is at the age when skills in dealing with others are crucial. And she needs your backup.
She is only "nearly five" and you're speaking of her lack of interest in her peers, "period," as if she is fully formed and fully fixed and will not change in this aspect of her personality. There is a world -- really, there's a whole universe -- worth of difference in who and how she is at this age and how she may be in six months, much less in six years. Peers become vastly more important to children -- even gifted ones -- as they get older, and she is not even elementary school age yet.
Please, talk to her teachers at her school and tell them what you have said here. Tell them, too, that you are thinking of homeschooling her apparently largely because she appears not to be interested in her peers. If they are wise and thoughtful and experienced, they will understand and not give you a knee-jerk "don't do that" reaction. They likely suspect that you are already not really satisfied with this school, because you're not, right? They would probably like the chance to talk about your daughter as a four-year-old, not just as a student. And please be open to what they say and receptive to the possibility that they may have some insights into her personality that a parent doesn't have. This is not a bash; this is just the fact that children behave differently in different settings, and unless you are present in the classroom every single day, you aren't seeing her as they see her -- interacting with her peers in class. It's normal for bright kids her age to be much more interested in adults and older children; those interactions are stimulating for them. But whether or not she's "interested" in her peers, she is indeed interacting with them, and the teachers may be able to fill you in on how she really acts with them when she's with them at school. They may not be on her academic level right now, maybe, and they may not play with her in the more fun and advanced ways that you or older kids can play with her. But they will catch up and she will need to know how to navigate friendships with children her own age, at every age.
It's interesting that you post that you're considering homeschooling "so that same age friendships aren't expected." Look back on Mamapedia for the many posts by homeschoolers saying how they work hard to ensure that their homeschooled children DO have same age friendships and do participate in group academics and other activities with other children their ages. Homeschoolers are very quick to say that their children are well socialized and have many activities with their peers, usually other homeschooled kids, through the many homeschooler groups and classes that exist.
And whether she is in a school or homeschooled: If same age friendships "aren't expected" at age four, when will they be? What is your longer-term plan for socialization and teamwork skills for her if you homeschool her?
Please be open to the idea that she will want her peers very soon. And please be open to the idea that she may indeed have more interest in her peers than you realize just now. She is barely out of toddlerhood and though she is mature, she is still very young. I had a very mature four-year-old too and she is still advanced, but she also is a little girl, and needs to be around other kids, in a world where adults don't always get to go.