I started work as a nanny in Jan, and since I wasn't given a W-4, I think I have to do a 1099 for 2020 taxes. Can I start paying taxes now instead of a lump sum in Jan?

I didn't work from March-September due to COVID-19 and I collected unemployment from May-September. I just want to make sure my 2020 taxes are in order since I did collect unemployment. Thanks