Retirement tax questions

My earnings are for a post doc fellowship stipend.  Earnings are reported on 1099-G. I think current law permits me to report this as taxable income.  If I do that using Misc 1099 form on Turbo Tax, the stipend amount appears on line 1 of the 1040 form which then permits me to make traditional IRA contribution followed by back door Roth IRA conversion.  If I do this, what do I do to show that the amount reported on 1099-G has been "re-characterized" as "Misc income"?

I appreciate your thoughts about this.  Thank you.