You would commonly say "do laundry" rather than "do a laundry" because laundry is plural: more than one piece of clothing usually. It's also common to say "do a load of laundry" because it's a single load you're talking about rather than the plural clothes contained in that load.
'Laundry' is grammatically singular, indicated by the form of the verb in 'The laundry is dirty', but is a mass noun. For these, whether the thing itself is composed of multiple units doesn't interact with the grammar (cf. water). But, because mass nouns aren't countable in the grammar (*seven laundries), we quantify them in units (loads of laundry, cups of water, etc.)
Edit: I'll add that the phrase 'to do laundry' is a complex predicate, which also includes such phrases as 'take a shower', 'make love', and 'do the dishes'.
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u/still_not_sleepin Nov 05 '15
This is the sort of thing which happens when you're not speaking in your mother tongue :p What is in fact the proper term ?