Supplemental Security Income Amendments of 1979 - Amends title XVI (Supplemental Security Income) of the Social Security Act to state that a disabled individual by reason of his or her earnings shall not be considered able to engage in substantial gainful activity, for the purpose of determining eligibility for SSI benefits, unless such earnings exceed the level at which the portion not excluded under title XVI equals the benefit that would be payable under title XVI if such individual had no income of any kind. Increases the amount excluded from the income of a disabled individual applying for SSI benefits by providing the following additional exclusions: (1) an amount equal to 20 percent of such individual's gross earned income representing expenses attributable to the earning of such income; and (2) such additional amounts of earned income of such individual as may be necessary to pay for attendant care services, medical devices and prostheses. Extends to the 15th month following the end of an individual's trial work period the time for which an individual may be considered disabled under title XVI. Stipulates that no SSI benefits may be paid for any month after the third month in which an individual engages in substantial gainful activity during such 15 month period. Considers an individual applying for SSI benefits presumptively disabled if within the four years preceding such application, such individual was treated under title XVI or title II (Old-Age, Survivors and Disability Insurance) of the Social Security Act as a disabled individual but ceased to be so treated because such individual engaged in the performance of substantial gainful activity. Stipulates that the performance of such activity may be taken into account in determining whether or not such individual is currently disabled. Lowers from 21 to 18 the age at which a parent's income ceases to be included in a child's income for purposes of determining eligibility for SSI benefits. Permits SSI benefits to be paid to individuals participating in approved vocational rehabilitation programs which will increase the likelihood that such individual may be permanently removed from the disability benefit rolls.