It's interesting how many people confuse the income tax and unified gift and estate tax systems. They are separate and distinct.
If you are asking whether you can deduct a gift from your gross income for income tax purposes, that would be a no, regardless of amount. But neither does your child have to report it as income.
What you are confusing income tax deduction with is the federal gift tax annual exclusion for gifts of present interests. If any individual gifts no more than $13K in aggregate gifts during the course of a calendar to another individual, and those gifts are of a "present interest" they are eligible for the annual exclusion, which is $13K this year but is indexed. To be a gift of a present interest, it must be available and usable by the donee. So gifts of cash are good. A gift in trust not so good unless the trust is designed to provide the donee with an opportunity to withdraw the gift immediately. These are known as "Crummey" withdrawal powers.
If you stay within the annual exclusion you do not have to file a Form 709 federal gift tax return.
In a recent case the IRS denied annual exclusion treatment to a gift of a limited partner interest on the grounds that as a limited partner the donee wan't entitled to distributions of income or withdrawal of assets, even though the gift was of the interest - not the income or property inside the partnership.
Keep in mind married couples can split gifts to double the annual exclusion.
There are, in addition to the annual exclusion, twoother important gift tax exclusions: education expenses and medical expenses.
I cannot comment on whether there are any GA gift tax consequences.
I generally agree with the answers provided by the previous post. I would like to add that Georgia does not have any gift tax, and that gifts made to individuals (such as the money and car gifts you mention) are not deductible from Georgia income tax. As with federal law, however, Georgia does not consider gifts income to the recipient.
Georgia does allow for an income tax deduction in some cases where a contribution to a special type of college savings account has been made, so if you have made any contributions to college savings plans you should consult a knowledgeable CPA when preparing your income taxes.