Companies like TurboTax can import data like W-2 if its available to them, but I believe entering the 1099-MISC is a manual operation.
While there is nothing wrong with estimating your 2019 tax bill andGenerally you should be paying it by January 15estimated tax throughout the year to avoid penalty,.
From IRS - Topic No. 306 Penalty for Underpayment of Estimated Tax:
thereGenerally, most taxpayers will only be aavoid this penalty if your underpayment is under $1000 OR you have alreadythey either owe less than $1,000 in tax after subtracting their withholding and refundable credits, or if they paid the IRSwithholding and estimated tax of at least 90% of your 2019 finalthe tax liability ORfor the current year or 100% of your 2018 (prior year)the tax liabilityshown on the return for the prior year, whichever is smaller.
See: How do I estimate my taxes when I have only 1099 income?
As you have had W-2 wages, if the Federal withheld exceeds what you made in 2018 and it sounds like you earned $0 in 2018 you should be fine. If you had interest or dividend income in 2018, you should pay enough just to avoid penalty.
If your earnings are done via contracting and still continuing, you are correct about paying quarterly estimated tax payments.
Do realize that most US states have state income tax as well so plan for that.
Given that IRS instructions for Form 1040 for 2019 tax year are not going to available under after January 15 you may wish to wait to file your 2019 Federal Income Tax.