The beauty of homeschooling is that there is so much flexibility if you need it. You could try it out for 1/2 of a school year at least, and if it didn't work out, she can go back to public school.
I homeschool my two elementary age girls and LOVE it. I love being right there with them and doing projects and field trips, along with the schoolwork. Ideally, you would be there with her, and can quit your job to do this. Maybe you could cut your hours down to part-time? You could have her do the more intensive schooling on your days off, or when you get off earlier.
It could still work out with you continuing to work full-time, though, if a number of factors work in your family's favor.
If she is mature for 12 years old (she should be 13 when she gets into 8th grade, right?), she could do her work while you are at work. The night before you could plan her curriculum, and go over anything she may not understand either that night or in the morning before you go to work. If she is the type of child who is a self-starter and doesn't need you checking up on her to make sure she is really working, this could work. She could also look after your 6 year old when he gets out of school (she could pick him up at the bus stop and babysit until you get home). This could be a great chance for her to show how responsible she is and what she is capable of. You could even pay her a small amount for the babysitting after school if you feel that she deserves it; however you may go by the family philosophy of everyone pitching in and not necessarily getting reimbursed for it). It will be a lot of responsibility for her to do her work on her own, then watch her brother until you get home, but she may be very capable of it, and enjoy it.
On the other hand, you may be reading this and saying, "I just don't know if she could handle it". You may find it overwhelming to go over her school things in the evenings, as well, with an almost 1 year old who needs your attention then.
That is a tough call. It definitely depends on the maturity level and personality of your daughter. Yes, more will be demanded out of you than if she were in public school, as well, but don't you think she might need help with her homework if she were in public school anyway? If she makes As without much help needed from you, you may find that she does very well at home without you.
Your biggest task will be getting her curriculum in order and creating a schedule/calendar of how much needs to be done each day/week/month. If she falls behind she could end up in a bad place scholastically. She may surprise you, though, and do very well, even farther ahead than you thought. You should know your daughter and what she is capable of.
If it doesn't work out after 1/2 a school year, put her back into public school. Something tells me that if this is something she really wants, she will make it work.
I have to add, is there something that might have happened at school to make her want to be homeschooled? Middle school years are tough and there can be social bullying and other issues at that age. Or is she just bored and understimulated at school, or perhaps doesn't feel like she relates to others well. If that is the case, you must help her deal with those issues by talking with a counseler.
But those are understandable reasons for homeschooling and I know families that have taken their daughters/sons out for social reasons and it changed their world for the better. But don't ignore the issue (if there is one).
I pray that you make the decision that is best for your family. God will reveal the answer to you by how peaceful you are with your decision.
Blessings,
S.