If I find a transaction that was recorded incorrectly in QuickBooks, can I change it even after paid 1st Q est tax?

It depends.  If your income tax return has been electronically accepted and the change will result in a decrease/increase in tax, you may need to amend (1040X) your income tax returns.  The amended returns can't be e-filed and must be mailled to the IRS and to your local state revenue.  You may adjust the estimated tax payments or leave it as is.

If you are asking if you can make changes in the QB bookkeeping system after sending in the first quarter estimated payment then  YES ...  corrections to the bookkeeping are always allowed.