In my experience Topology is not a overly difficult course when it comes to the lectures and key ideas/theorems, but the exams can be a right ***** sometimes (but this is all obviously subjective)

I prefer topology infinitely more than I do probability, and find the topology lectures easier to follow and more interesting, but when it comes to exams probability questions are so much easier.

The course you described looks similar to the first part of the course I took. A lot of real analysis-ey stuff at first but persevere!

I definitely recommend topology, it was one of my overall favourite courses and has some really interesting ideas.