Yes, money earned from a part time job will qualify you to be able to contribute to a Roth IRA.

Please follow these steps to enter your 1099-R and conversion:

1. Open your return
2. Click on "Search" on the top right and type “1099-R”
3. Click on “Jump to 1099-R” and enter your 1099-R as shown
4. Answer questions until you get to “What Did You Do With The Money” and choose “I moved it to another retirement account”
5. Then choose “I did a combination of rolling over, converting, or cashing out money.” and enter the amount next to "Amount converted to a Roth IRA account"
6. Continue answering the questions in TurboTax

Be sure to enter a basis when asked if you had nondeductible contributions in your traditional IRA in the past.

I won't be receiving a 1099-R for my new ROth opened in jan 2021 for my 2020 taxes. How do I enter info for my 1099-R -- or is this not permitted??

If you did the conversion to the Roth IRA in January 2021 then you will have to wait until you get your 2021 1099-R and enter it on your 2021 tax return. You will not enter this on your 2020 tax return.