My view is that "infants" refers to the true disciples that Jesus had.
It is commonplace to let Scripture interpret Scripture. Ergo, I will provide a few verses to support my view.
Firstly, John says that whoever believes and accepts Jesus is given the privilege of becoming a child of God.
12Yet to all who did receive him, to those who believed in his name, he gave the right to become children of God— 13children born not of natural descent, nor of human decision or a husband’s will, but born of God. John 1:12-13 NIV
So we learn here that it is whoever that believes that become like a child.
16But Jesus called the children to him and said, “Let the little children come to me, and do not hinder them, for the kingdom of God belongs to such as these. 17Truly I tell you, anyone who will not receive the kingdom of God like a little child will never enter it.” Luke 18:16-17 NIV
Also, those who wish to get into the kingdom must accept the kingdom like a little child as you can see from the verse. So the servants/subjects/citizens of the kingdom are like little children. That means since the disciples of the kingdom are like little children, they could be referred to as such in metaphor. Moreover, there is one especially damning (pun not intended) evidence to the fact that the "infants" being spoken of here are the true disciples of Jesus.
42And if anyone gives even a cup of cold water to one of these little ones who is my disciple, truly I tell you, that person will certainly not lose their reward.”
Matthew 10:42 NIV
The context here is that Jesus is talking about the persecution that the disciples will face in their life when they preach the gospel to the nations. So he directly refers to a disciple as "one of these little ones", which sounds extremely close to "infants" (probably a result of translation differences).
Catholic Church's Perspective
So onto the second part of your question, I believe that the Catholic Church would agree with me. If not because of my reasoning and the context of the passage referring to his disciples and his ministry, then because that one of their own venerated Saints said
“Whosoever is a LITTLE ONE, let him come to me.’ (Proverbs 9:4) And so I succeeded. I felt I had found what I was looking for. But, wanting to know, O my God, what You would do to the very little one who answered Your call, I continued my search and this is what I discovered: ‘As one whom a mother caresses, so will I comfort you; you shall be carried at the breasts, and upon the knees they shall caress you.’ (Isaiah 66: 13,12) Ah! Never did words more tender and more melodious come to give joy to my soul. The elevator which must raise me to heaven is Your arms, O Jesus! And for this I had no need to grow up, but rather I had to remain little and become this more and more.” - St Therese of Lisieux
The source of that quote is found here.
Since a saint was referred to as a little one in her own words, she must have been taught or taught that a disciple/believer was to be like a little one, and therefore must have perceived the verse in Luke 10:21 as a reference to the believers and disciples of Jesus.
As of what exactly they teach on this, there is always the chance to ask Catholic priests either in person and even online! I'm sure they would agree with something along the lines of the answer given under My Perspective. Thanks for reading and I hope this answers your question!