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What you describe qualifies you as Head of Household status. 

However, your 19 year old daughter MUST be a full time student.  More information here: https://turbotax.intuit.com/tax-tips/family/guide-to-filing-taxes-as-head-of-household/L4Nx6DYu9

Also, review the IRS information to be sure.  https://www.irs.gov/help/ita/what-is-my-filing-status

 

Sorry for the loss of your wife.