Plumbing help?

Alright y'all, not sure this is the right group for this but I couldn't find one that I thought it might be better in. Anyway. We moved into a new (to us) house last December. It's a 1-bath house so the only sinks we have are the kitchen and bathroom (obviously there's a tub/shower too). Whenever my infant son has a blowout, which is incredibly often, I have to use the hose outside to spray the poop off and scrub the stain on the front porch. I feel like a redneck when people walk by 🤦🏼‍♀️ but I don't want poop in my bathroom sink and definitely not my kitchen sink. His poop is also chunky so I don't want it in the bathtub getting caught in the drain. 🤢 We have a utility room downstairs which is a concrete floor with a drain and has our washer, drier, furnace, water heater, etc. We would love to install a utility sink in there in order to scrub clothes and stuff. The water line is in the room next to the washer. How easy would it be for us, with no plumbing experience, to install the sink ourselves? We're always looking to save a buck and learn more about maintaining a home and plumbing is a good thing to learn. I know this post was long but thanks for reading to the end and TIA for any advice!