Deciding whether to dust or vacuum first is a valid house-cleaning concern. It seems reasonable to assume that because dusting may send a certain amount of dust to the floor it is better to dust first and vacuum second. But, as you will find out, that may not be the best sequence.
Dusting and Vacuuming
When cleaning the kitchen, for instance, it makes sense to clean the counters before you sweep and mop. This is because you may inadvertently or intentionally send crumbs and other debris to the floor to sweep them. With dusting and vacuuming, however, it is a little different. Since vacuuming typically kicks up a lot of dust that is not sucked up by the vacuum, it is better to vacuum first and then dust. After running the vacuum, give the dust a few minutes to settle, then go in with the Pledge and the dust rag. The exception is if you use a HEPA filter. It is capable of capturing very small particles. In this case you may want to dust first and then vacuum, ensuring the vacuum sucks up the most dust particles.
Whatever the sequence, you should dust and vacuum at least once per week. The reasons for this are evident especially if someone in your household has allergies. Letting too much dust build up can aggravate allergies or asthma. Vacuuming does the same thing for the carpets which are notorious for gathering dirt and other imperceptible debris.