In normal conversations, we commonly use the expressions “do the dishes”, “do the laundry”, or “do the housework”. We can omit the article to put the emphasis on the activity rather than the items to be washed or cleaned.
When using the expressions “take a shower” (American English) or “have a shower” (British English), we always include the article “a”. It is not possible to omit it or use the article “the” instead.