I have worked with gifted children and I would like to focus on them once I am more qualified. I feel that the best thing that you can do (outside of hiring a professional) is still send her to kindergarten but with reduced hours. explain to her (constantly) that she is going there to learn and socialise with other children. Emphasise that she is there to play and have fun and practice listening to the teacher and following the rules for when she goes to big school.
Aim for half-half if you can, as in half the time that she goes to kindergarten but then focus the other half with a private tutor or very qualified nanny. Ask which ever school you plan on sending her to when she is older for some advice on the curriculum, get as much information as you can and pass that on to your tutor/nanny.
I also recommend taking her to outside activities frequently. Take her exploring, expose her to as much as the world as you possibly can. Explain, in depth, the WHY and HOW of any questions she might ask you along the way. As she gets older try to prompt the why/how question as much as you can, for example suggest that she ask the post office lady how the mail system works and why it is an important system.
The biggest NO I can tell you is not to baby her. Don't give her the answers that most parents give their children. I.e she asks you why you like ice cream? Don't just say "because it's yummy". Take your time to really think about the answer and then tell her the entire truth, maybe "I like ice cream because it tastes good, and it makes me feel good. It also reminds me of when I was a little girl, my father used to take us to the icecream store for a treat when we were well behaved. Eating icecream is very nostalgic to me.". Also, if you take your time to think about the answers she will realise that you do hold value to her questions, and she will want to ask you more. So don't be afraid to stop and think.
If you want her to mature quickly to prepare her to enrol in a full time gifted education course then make sure that are always explaining her feelings to her. Don't say "You are angry because you didn't get icecream today, you need to stop being silly or else", that's stupid and oppressive. Say instead "I think that you might be feeling angry right now. When I get upset about something that is unreasonable, like when I dont get to watch my tv show because daddy is watching the football, I often feel angry as well. It took me a long time to realise that I shouldn't really be angry at daddy though, because it is not his fault. I understand how you feel, and I want you to know that it is absolutely ok to feel that way - as long as it doesnt hurt somebody else, or yourself.". Even if she doesnt listen, make sure you explain it in a clear and calm voice.
For discipline you want to emphasise that you trust her to make her own responsible decisions. If she is being naughty, explain what she is doing, tell her that it is unacceptable behaviour and explain why, offer her an easy alternative and tell her that you are giving her an opportunity to make her own decision about what she is doing, and that you trust her to act responsibly. If she makes the right decision never ever use that against her i.e if she does something else later that day that is naughty don't say "you were doing this earlier and now you are doing this, I am fed up". Instead say something like "This morning you made a responsible decision and I am very proud of you for doing that, I would like you to think about how you are acting now and tell me if think that what you doing is acceptable behaviour."
Discipline is tricky with gifted children... Just make sure that you remain constant, calm and in control.