1) absolutely you should get life insurance. at minimum get a term life insurance policy--for you and your spouse. that way if something should happen to one or both of you, your child is protected. term policies are relatively cheap, especially if you are in good health.
2) get a living trust. this is a legal document that not allows you to declare your own medical decisions but also allows you to give your money to your child without losing 10%-15% of it to probate court--a ridiculous fee that just takes money away that should go to your child.
3) start a 529 college savings plan. even though it's a college savings plan, really you can use it for any educational purpose after your child turns 18. it doesn't have to be for college. it can be for vocational school. it can pay for rent while she goes to vocational school. it can be used for graduate school. it can be transferred to a sibling or to a niece or nephew. best of all it grows TAX-FREE and is withdrawn TAX-FREE as long as it is withdrawn for any educational/living expense use for your kid. this really is the no-brainer investment vehicle for people with kids.
4) the moment your kid makes any kind of money, even if it's just a little bit from working at a fast food place and she gets a paycheck, open a roth IRA account for her and contribute the maximum every year. this money compounds interest TAX FREE.
5) most importantly: the best way to save for her is to wisely save for YOURSELF. take care of your retirement. her financial future is bright if your financial future is bright. if you have wealth and don't need to depend on her to pay your bills or mortgage when you retire and get old, then obviously she comes out ahead. if you have money to bequeath to her upon your death then she obviously comes out ahead. if you have extra money that can help pay her tuition so she doesn't have to have student loans or if you can help her with a down payment on her first house years down the road--that's the kind of stuff that really sets her up. save money for you and you are saving money for her.