Yes. You need to report unemployment. You can call the Department of Labor in your state and request another copy.
Additionally, the IRS will not start processing returns until February 12, so waiting for this form is not slowing down your return.
1099 forms for unemployment are done by states, so there will be lots of different processes for the different states.
I live in Illinois, and the process is completely confusing. The IDES software has a whole 1099 section, where they have lots of instructional text but it doesn't match how the site behaves. The site actually behaves reasonably well, just not how the instructions describe it!
The 1099 section in Illinois uses the same username and password as what you use to log in and certify for unemployment.
Two weeks ago the site said that the 1099s would be available "at the end of January" and had a place to sign up to receive yours electronically. The site says that you get an email when they are ready. I have not received any emails, but when I logged in this morning my info had appeared at the bottom of the page and there was a button to push to download my 1099.
So, anyway, depending upon the IT capabilities of your state's UI department, your 1099 MIGHT be available, and there MIGHT be instructions that are correct. But it is definitely worth poking around to look for it.
Most people on unemployment in 2020 already know that the UI systems in every state are completely swamped by the sheer volume of unemployed people, all of the rules changes from the CARES act, and the sharply increased volume of UI fraud as bad guys have tried to use the general chaos to get away with stealing. So you need to either wait a bit for the form to just show up in the mail, or do your own research. For heavens sake don't try to contact them because they are really busy!