Well, yes an no …accountability is just a reference to understanding. And it is necessary to understand if we are to accept the new covenant (Rom 10:9) and be baptized in the spirit.
For my kids it was age 6 & 7 that they accepted Jesus as their Lord and both spoke in tongues….but it varies with the individual.
Prior to accountably (understanding) they are sanctified by their parents 1Co 7:14.
If it is your position that Romans 10:9 means that one must be capable of having a certain level of understanding of the Christian faith; then what do you do with those who are unable? Or who, perhaps, have an insufficient understanding, or perhaps are mistaken?
I don't believe that Paul's point here is that we can't be saved unless we are capable of having "understanding", rather Paul's point is what he goes on to say:
"For the Scripture says,' Everyone who believes in him will not be put to shame.' For there is no distinction between Jew and Greek; for the same Lord is Lord of all, bestowing his riches on all who call on him. For 'everyone who calls on the name of the Lord will be saved.'" - Romans 10:11-13
Paul is saying that the Gospel is for both Jew and Gentile, after all that is the entire thesis statement of Romans, "For I am not ashamed of the Gospel for it is the power of God to save all who believe, the Jew first and also the Greek." (Romans 1:16). Because, as he continues in the same place, "By the justice of God is revealed from faith to faith, just as it is written, 'The just shall live by faith.'" (Romans 1:17).
All who call on Jesus, all who hear and believe (Romans 10:14-17), will be saved. God does not favor one people over another; for both Jew and Gentile, for slave and freeman, for young and old, Jesus and what God has done through Jesus is for everyone; that through faith we might be justified on Christ's account (Romans 5:19).
But this legalistic reading of Romans 10:9 of yours turns the message of good news for all sinners to an obstacle that we must overcome by our own power and will. Though, he has clearly taught elsewhere that "It is by grace that you have been saved, through faith, and this is not of yourselves, it is the gift of God; not of works, so that none may boast." (Ephesians 2:8-9).
Calling on the name of the Lord, believing upon Him, is not a work that must be accomplished by human ability and understanding; but is the power of the very Gospel itself to create faith in us, that we look to and depend upon Christ, have faith in Christ.
It's not about us. It's about Jesus Christ.
The alternative, I imagine, is that children and those who don't understand (say those with learning disabilities) have an automatic salvation of some kind. In which case, you just undermine your own position that one must confess with their mouth and believe in their heart.