She's 3 years old. Wouldn't she be the beneficiary though because if something were to ever happen to me, I want to leave her the life insurance money.
So instead of her being insured shouldn't it be me that is insured and her the beneficiary?
If you insure your daughter's life, then that means the life insurance policy pays out a death benefit if she dies.
If you want to have money for her if you die, then you want to get life insurance on your life.
You may want to consider using the life insurance death benefit to set up a trust to benefit your daughter, and leave someone you trust, as trustee of the trust for your daughter.
If you leave the money to her, whoever gets custody of your daughter after you die, gets control of the money.
Also, since you have a minor child, you may want to set up a will, with guardianship intentions for your daughter - although if her other parent is still alive, they'd pretty much automatically get custody of your daughter.
Here's a guide to buy term life insurance coverage online.