Either is fine, as long as 'the clothes' is obviously 'our clothes' based on context. In other words, if you were clearly talking about your family, then 'the' is OK. If (say) you were talking about someone at a laundry, it isn't. That is the beauty of 'the'. We use it when we think that it is clear what we are talking about, and don't need to repeat it.

What about do the laundry? "She does our laundry?:

I've learned just this expression

She washes our clothes