Where do I put the date my payment will be made so that my underpayment is calculated correctly?

That is at the end right before you file.  But that won't affect the penalty on 1040 line 38.  

It's not for filing or paying late.  It doesn't have to do with last year's tax return or not paying estimates for this year.  The penalty is an "estimated" amount.    It's a penalty if you owe too much or for not paying in enough withholding during the year or not paying in evenly.  Even if you are getting a refund you can still owe a penalty.  It's very common and normal and expected for the IRS or state to bill you for more or send you a refund.

You might be able to eliminate it or at least reduce it.  You can go to Federal Taxes tab or Personal tab, under Other Tax Situations and select Start by the Underpayment Penalties. You will answer a series of questions that may reduce or eliminate the penalty. Or you can elect to have the IRS figure the penalty for you.  It's form 2210.

It's under

Federal or Personal (for Home & Business Desktop)

Other Tax Situations

Additional Tax Payments

Underpayment Penalties - Click the Start or update button