Do I have to put "doing" ? No...
What do you look forward to at the weekend ?
does this sound right? Yes...
Without "doing", the questioner expects a simpler more general answer:
- I look forward to a bit of peace and quiet. I look forward to just sitting around and maybe reading or watching movies. I look forward to being with my family.
With "doing", the questioner expect a little more detail about the activities that you would be doing at the weekend:
- I look forward to playing with the children. I look forward to to doing barbecues and hanging out with my friends. I look forward to going on hikes in the mountains with my family.
So, you see, there is not a big difference between these two questions. They are both good.👍