I'm going to advise against the divider until AFTER they have started free swimming and look like a small moving cloud of babies. In my experience, the parents take much better care of the eggs than any human can. They constantly fan the eggs to make sure they stay clean and have oxygen. Also, there will be unfertilized eggs and the adults will remove those and any eggs that didn't make it. By doing this, the parents prevent the spread of fungus.
However, once they become free swimming, there is a risk that the parents will become stressed and eat the babies. This is when I would separate them.
I wouldn't worry too much about losing the babies though. You have a confirmed spawning pair so you'll gets lots of babies! You might want to separate the female and male once you get the fry safe and that way she will have some time to herself to recover.