For sucking up dust, you naturally choose a vacuum cleaner, complete with filter and special nozzles for great use. But when emptying a fireplace, it is not wise to use an ordinary hoover. In that case, opt for an ash vacuum cleaner.
An ash vacuum is specially made for sucking up ash. They have a sturdy collection container and a built-in fireproof safety system. A nice addition to have in your home if you like to light the fire or barbecue often.
Note: you should never suck up smouldering ash. Always let it cool down before sucking it up.