An Estate tax year begins on the day after the death of the individual and cannot exceed 12 months.
Per IRS Publication 559, Survivors, Executors, and Administrators, page 15:
Income Tax Return of an Estate - Form 1041
An estate is a taxable entity separate from the decedent and comes into being with the death of the individual. It exists until the final distribution of its assets to the heirs and other beneficiaries. The income earned by the assets during this period must be reported by the estate under the conditions described in this publication. The tax generally is figured in the same manner and on the same basis as for individuals, with certain differences in the computation of deductions and credits, as explained later.
The estate's income, like an individual's income, must be reported annually on either a calendar or fiscal year basis. The personal representative chooses the estate's accounting period upon filing the first Form 1041. The estate's first tax year can be any period that ends on the last day of a month and doesn't exceed 12 months.
Generally, once chosen the tax year can't be changed without IRS approval. Also, on the first income tax return, the personal representative must choose the accounting method (cash, accrual, or other) to report the estate's income. Once a method is used, it ordinarily can't be changed without IRS approval. For a more complete discussion of accounting periods and methods, see Publication 538.
Special rule in case of death. A taxpayer's taxable year ends on the date of his death.