숙제를 할게요 is a right expression for I am going to do my homework but in a daily speech it is more natural to drop out the objective particle '을' and simply say 숙제 할게요. The difference between 숙제를 할게요 and 숙제나 할게요 is a tricky subject. We use this auxiliary particle, 는 to imply that the speaker made the choice even though it was not the best or satisfactory because he could not find an alternative. I had a hard time to find an equivalent expression in English but failed. So if I translate 숙제나 할게요 into English, I would be this kind of lengthy sentence, "I am going to do my homework as there is nothing else to do."