Military Widow's Tax Elimination Act of 2019 This bill modifies the Department of Defense's Survivor Benefit Plan and how it operates in relation to other benefits. The plan currently provides a monthly annuity (based on a percentage of a service member's retirement pay) to an eligible beneficiary upon the death of the service member. Currently, if a surviving spouse is also entitled to dependency and indemnity compensation, the annuity paid under the plan will be reduced. The bill repeals certain provisions that require the offset of the plan annuity from amounts paid in dependency and indemnity compensation. Under current law, upon the request of the surviving spouse, the military branch concerned is authorized to pay an annuity to the service member's dependent children instead of to the surviving spouse. The bill restores the annuity to an eligible spouse who previously elected to transfer payment to a dependent child.