If I was to gift my goddaughter a piece of property for $1 will I have to pay IRS tax on this?

At the present time, there is a $5,000,000 exclusion from federal gift taxes.  However, you should obtain the advice of a professional who has expertise in this area of tax law who can advise you based on all of your particular circumstances.  The reason I make this suggestion is because there are a variety of factors to be considered in any question involving gift and/or estate tax law.  For example: the federal gift and estate taxes are "unified" which means that the $5,000,000 exclusion pertains to the total of taxable gifts over the donor's lifetime and his estate upon his death.  These calculations are complicated; they require the application of several provisions of the tax law, and a substantial gift should only be made after careful planning and with the advice of a competent tax advisor.  In addition to the federal gift and estate tax, many states impose their own gift tax; and the exclusions vary from state to state.  The exclusions from state gift tax are generally far smaller than the current exclusion from federal gift tax.  Therefore, you should obtain professional advice on the potential impact of any state gift tax that may apply to the gift that you are considering.