Is this the doctrine of the Catholic Church?
It is an oversimplification that can lead one to false ideas.
First, "salvation" to Catholics doesn't mean the same thing that it does for Protestants. Thus, if I say "Baptism saves", you will immediately think we believe we go to heaven because of this one-time event. The correct term is "justify". We are made children of God, inheritors of heaven, infused with God's Grace and forgiven of all sin. If we were to slip and fall in the Baptismal font and die, we'd be in heaven. But for the rest of us, our eternal salvation is not secured as a result of ONLY Baptism.
The Gospels (and Paul, if one drops Sola Fide as their lenses for looking at the Scriptures) are clear that we must have faith in God, trust in His promises, and obey Him out of the sake of our love for Him. When doing deeds of love, it is understood that God is present within us, as we cannot earn righteousness on our own. God enables us to "work out our salvation", as He places within us the will and ability to do His will (Phil 2:12,13).
Someone brought up the Young Rich Man previously. That is one of many examples that Jesus gives us about what we must do to enter the Kingdom. He told the man "you are not far from the Kingdom" when the man said he obeyed the commandments. Jesus looked at the man and loved him - presumably, because he was not like the Pharisees who did good works BUT expected payment/wages. The man obeyed the commandments out of love for God. "He was not far from the Kingdom" But Christ saw another attachment - money - that kept the man from entering God's Kingdom. Faith is nowhere mentioned in this story. HOWEVER, it is PRESUMED, since the man was obeying the commandments out of love.
One can be saved only through faith in God, working out his faith through love (Gal 5:6). Without love, I am nothing (1 Cor 13:2). Faith without works (of love) is dead (James 2). Thus, BOTH are needed - faith AND deeds of love. Since justification is NOT a one-time process (we are not always righteous in God's eyes), we must persevere in our faith and love in God. God gives us the grace to continue on this journey, which we call sanctification. The two terms go together.
An interesting analogy that might help is this...
Think of a person as a glass full of black liquid, representing our soul before God's graces come to us through Baptism. God, from Baptism, pours His Spirit into us (the glass), adding white liquid and completely whitening the liquid in the glass. Now, as time goes by, we, by our sin, add black liquid back into the glass. It darkens a bit. When we ask for forgiveness, repent, and love others, God pours some white liquid back in. As we continue to grow in holiness, we add less black liquid in, while God continues to add white liquid. The day we die, God will judge the color of the liquid. Note, we NEVER add white liquid to the glass! We ONLY can try to keep the black liquid out. By turning to God, He gives us a stronger will, enabling us to resist temptation and to love others without thought of reward (as we can never earn a reward).
Some may ask "well, how do I know if my "glass is white or black"? Don't be scrupulous like Luther...If a person is sorry for the sins he has committed, this is the work of the Spirit within us - thus, we are not being shunned by God. Hope this helps
Regards