Do I Need To File Quarterly Estimated Taxes for Wife's Business in 2019?

Hi:

As to your first question, here is a link to review and compute any possible NOL carryovers.  There are some new rules that took effect for years after 2017. 

https://www.irs.gov/publications/p536

As to your second question, yes, it will be a good idea to make estimated payments for your spouse's business.  Not only will there be income tax that will have no withholding, but there will also be self-employment tax that will add to your tax burden and there will be no withholding for it.

As to any penalties, missing the April 15th deadline for ES payments does not necessarily result in penalties.  When the 2019 is filed in 2020, the total amount owed after considering all withholding(s), credits, pre-payments, and estimated payments must meet a certain threshold before an estimated tax payment penalties are applicable.

https://www.irs.gov/businesses/small-businesses-self-employed/estimated-taxes

Penalty for Underpayment of Estimated Tax

If you didn’t pay enough tax throughout the year, either through withholding or by making estimated tax payments, you may have to pay a penalty for underpayment of estimated tax. Generally, most taxpayers will avoid this penalty if they owe less than $1,000 in tax after subtracting their withholdings and credits, or if they paid at least 90% of the tax for the current year, or 100% of the tax shown on the return for the prior year, whichever is smaller. There are special rules for farmers and fishermen. Please refer to Publication 505, Tax Withholding and Estimated Tax, for additional information.