A 1041? Decedents Will directed the Estate pay taxes on Estate Income earned. Can the Estate via 1041 pay federal income taxes due and thus no K-1s issued?

The Estate will earn between $20-25 K of income.  Most  of the income is dividends and Capital Gains from Stock sales after death. Does the 1041 allow for paying taxes due or do K-1's have to be issued to distribute income to beneficiaries.