It would be to say that they are worthy of heaven when they are born up until some point where they start sinning.
Not at all! (though that appears to be the Baptist "age of accountability" position). Even were it possible to be sinless, that would NOT entitle someone to go to Heaven. Heaven is not merely awarded for a lack of sin. That's like saying I should get a promotion because I didn't do anything to get fired. Adam and Eve were not bound for Heaven prior to the fall, they were merely creatures, not adopted children of God. The Cross does far more than merely remove sin.
And I don't think "sinless" is the right word for infants. Newborns merely lack actual personal sin (but it doesn't take long).