This a libertarian response, not a Catholic one.
No, it is quite Catholic.
Income inequality exists, just like every other kind of inequality exists on this earth. People have different IQ, talents, abilities, experience, training, etc. and this translates -- rightly so -- into different levels of material wealth.
Our Lord said, "The poor you will have always with you." and He wasn't against relieving them -- but He defended the spending of money on religion, worshiping God, etc. Because you can't eradicate poverty, any more than you can stop people from being stupid. As long as people will fall for brain-dead scams, walk into pawn shops like sheep to the slaughter, etc. you will have poor people. As long as you have free will (Shall I study, or watch this movie?) you will have people making poor decisions, and working lower-paying and dead-end jobs as a result.
Even if the world transitioned from fiat currency (which is constantly debased through inflation) and switched to sound money, the problem would still exist: the job of money is to match the producer with the consumer. But not all goods have the same value, and not all occupations are equally valued either. The guy with a wide knowledge of medicine, illnesses, and surgery is going to be paid more "whatever" than the guy who sweeps the floor. Anyone can sweep a floor. Only a few can become a doctor.
It has always been so, from time immemorial, and always will be.
Dreamers like Karl Marx preached an end to all private property to "remedy" this "injustice", but what came from him (Communism) turned out to be a sick joke -- replacing our capitalist masters with a new oligarchy at the top. (See the book "1984" how the Inner Party members living in luxury while the common man is quite poor) "All Animals are equal - but some are more equal than others." And what do you know? That's exactly how it was in Communist Russia. The Communist dream of "each gives according to his talents, each takes according to his needs" is a pipe dream in practice.
Read "Animal Farm". At the end, even the prime rule, "Four legs good, two legs bad" is broken by the pigs, who complete the circle by beginning to walk to two legs -- just like the human masters they ousted. A very good parable about Communism. If you haven't read it yet, you should.
George Orwell was a smart man.
Have you read Rerum Novarum? That speaks about this topic as well. Both rich and poor have a role to play in society, in God's plan. Both should submit themselves to God, His will, and His providence -- not succumb to class envy.