As a 1099 contractor your wife is self employed, so unless she incorporates her business she'll be filling out Schedule c.
She'll owe self employment tax which is both employee and employer parts of FICA, so 15.3% (sort of, there's a multiplier to avoid some circular logic around not paying tax on the tax, but close enough -- look at schedule SE if you want to be exact).
Otherwise you will owe tax on her income just as you would on any additional income with two exceptions: 1) you can deduct 1/2 of self employment tax and 2) as of the new tax law you can deduct the lesser of 20% of her qualified business income (if your taxable income is under $315k, otherwise this is a maybe) or your taxable income minus capital gains (how exactly this works is still up in the air).
There are a number of safe harbors under which you can avoid an underpayment penalty:
- You owe $1,000 or less in tax after subtracting withholding and refundable credits,
- You paid withholding and estimated tax of at least 90% of the tax for the current year
- You paid 100% of the tax shown on the return for the prior year (110% if your AGI is over $150k)
You'll still owe the tax, so make sure you have some sense of what you'll owe so you can have that saved in time to pay your taxes, but as long as you will meet a safe harbor you don't need to worry about estimated taxes. You can pay taxes from any combination of withholding and estimated taxes. It matters when you pay estimated taxes (pay them all in the 3rd quarter when you should have paid some in the 1st and you'll owe a penalty), but withholding can happen any time in the year.
I'm self employed and my wife is not, so we set up her withholding so that it hits 100% of the amount we owed the previous year.