Is it possible to file two tax returns (mine plus my minor dependent) from the same account?

When you use Online TurboTax, you get one return per fee.  Each return needs its own account and user ID.   If you use the same account and user ID for a second return, you overwrite the first one and lose it forever.

https://ttlc.intuit.com/community/using-turbotax/help/how-do-i-start-another-return-in-turbotax-online/00/25596

It depends.  You can do that with TurboTax Desktop by simply starting another return and if you use TurboTax Online you simply create a new account for your child.

@bwcross