"The immunity from original sin was given to Mary by a singular exemption from a universal law through the same merits of
Christ, by which other men are cleansed from sin by baptism. Mary needed the redeeming Saviour to obtain this exemption, and to be delivered from the universal necessity and debt (
debitum) of being subject to original sin. The person of Mary, in consequence of her origin from Adam, should have been subject to sin, but, being the new Eve who was to be the mother of the new Adam, she was, by the eternal counsel of
God and by the merits of
Christ, withdrawn from the general law of original sin. Her redemption was the very masterpiece of
Christ's redeeming wisdom. He is a greater redeemer who pays the debt that it may not be incurred than he who pays after it has fallen on the debtor.
Such is the meaning of the term "Immaculate Conception."
From the texts Proverbs 8 and Ecclesiasticus 24 (which exalt the Wisdom of
God and which in the liturgy are applied to Mary, the most beautiful work of
God's Wisdom), or from the Canticle of Canticles (4:7, "Thou art all fair, O my love, and there is not a spot in thee"), no theological conclusion can be drawn. These passages, applied to the
Mother of God, may be readily understood by those who know the privilege of Mary, but do not avail to prove the doctrine dogmatically, and are therefore omitted from the Constitution "Ineffabilis Deus". For the theologian it is a matter of conscience not to take an extreme position by applying to a creature texts which might imply the prerogatives of
God."
Nope, it doesn't appear that catholicism has any news on Mary's baptism. But they do view her as being exempt from "original sin," which is the primary sin which is cleansed in catholic baptism, and they view her as being the spotless woman mentioned in Song of Solomon, thus baptism would probably not be required to remit sin.
St Thomas Aquinus, however, wrote in Summa Theologica that he doubted that Mary was eternally sinless, since she was redeemed by Christ, and a sinless person has nothing to be redeemed from. Summa III:27:2, ad 2