Anti-Inflation Tax Act of 1979 - Amends the Internal Revenue Code to require annual cost of living adjustments to: (1) personal income tax brackets; (2) the $1,000 personal tax exemption; (3) the adjusted basis of property for purposes of determining gain from the sale or exchange of a capital asset; (4) interest rates on savings bonds and certificates issued pursuant to the Second Liberty Bond Act and other obligations of the United States; (5) withholding tables; and (6) minimum income levels for which income tax returns must be filed.