אני עושה שיעורי בית is also correct.
Which of them would be preferable?
A specific verb (such as מכין) is usually considered better than the generic do=עושה. In school the teachers would correct us if we said עושה, but it's pretty common.
Thank you ;)
Both are equally good IMO.
In my ulpan in Israel, we never had שיעורי בית. It was always עבודת בית. Maybe a regular Israeli school uses שיעוים.