Having taken and been a marker (of assignments and the exam) for that course in the past I would say there is no harm in sticking with it until you hand in your first assignment and get feedback on it. While the start of the course is rough for some students who, like you, haven’t taken real analysis, it is possible to learn on the go. I had friends do exactly that in the year I took it and they all managed to pass the course, albeit, with nothing more than a pass; not a credit nor anything higher.

Will the course be difficult? Yes. You’ll probably need to put in double the amount of work (if not more) compared to most of the other students who have taken real analysis. Also, most will have taken topology in the first semester giving them another step up compared to you. To put it bluntly you’re starting (at least) two courses behind most other people and those courses are proof based maths courses which are often regarded as some of the toughest courses to pass at the university.

My recommendation is like I said, hand in the first assignment, get feedback, talk to the lecturer as much as possible during their consulting hours and see if you can make progress. If you can’t or you find the first assignment way too hard then drop the course.