Since none of the answers were quite right, I'm answering my own question from what I've learned since posting.
First off, if you earn a lot more in one year like this, you don't need to do any real calculations to avoid underpayment penalties. You simply need to pay the at least 100% of the last year's tax (110% if AGI is above a threshold which I don't remember). Secondly, the first payment is only for income earned in Jan - March, so in my case, since the house sold in April, I get a reprieve until June.
Of course, you might want to at least estimate the amount in order to make sure you have enough to pay it when tax time comes around. The IRS frowns on not paying the full amount.
