This really depends on the professor and the class. For a lab class, I would say it's completely inappropriate. For other classes, it depends.
I think even many teachers who would be okay with it as a one-time thing in an emergency would be opposed to this being your usual child-care plan. I'd also suggest that bringing a baby to class is a short-term solution at best. A semester is three to four months long. In that time, a six month old baby goes from an occasionally noisy, basically stationary object to a creeping, crawling, possibly even walking person, requiring more and more of your attention.
I'd look around for off-campus childcare options, or a sharing arrangement with other student moms. UIC is not a small school, you can't be the only one.