You don't get an extension for quarterly payments.
I would go ahead and make a 30% or 40% payment (depending if your total yearly income after deductions will be less or more than $74,000) under her SSN on the IRS payments site.
This will be correct both if you keep her business as a schedule C business, or if you add her to the LLC. (Because, partnership income is reported to the partners on a form K-1 and does not have withholding, so the partners still must make estimated payments.)
