For same year contribution, isn't that technically just a recharacterization?
Also IRA to IRA isn't a backdoor Roth. Unless we're missing some details.
A backdoor Roth involves a tIRA to Roth IRA conversion. And even in the same year, you can do a conversion. Indeed, a recharacterization wouldn't work here, because OP's income presumably disqualifies him or her from making regular Roth IRA contributions.
Backdoor Roth steps:
1. Contribute to tIRA. Don't take the deduction for doing so.
2. Convert to Roth IRA. Since you didn't deduct in step 1, you're only taxed on earnings.
There is also a Mega-Backdoor Roth that involves after-tax (not Roth) contributions to your 401K.