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I wanted a more definitive answer, with a cite.  I found two answers on the net:

 

"The first return for the the irrevocable trust is filed for the period beginning with the date of the death (of the last parent) and ending on Dec. 31 of the same year".   By Mary Kay Foss, CPA at calcpa.org

 

"If the grantor dies Sept. 13, you have to report the trust's income from Sept. 13 to Dec. 31".

From finance.zacks.com

 

These two answers support my belief that I should use the date of death of the last surviving parent as the beginning date of the calendar year tax period at the top of the 1041.  This is for the initial tax return for an irrevocable trust.