When cleaning your house it's best to dust the house and use a damp cloth to help wipe up the dust to prevent it from flying through the air.
Then after dusting and wiping down the dust you can vacuum the carpets because the dust would settle into the carpets.
But if you want to vacuum and then dust it's okay as well but if you vacuum and then dust then you will have to vacuum again to get the dust out of the carpet.
Instead of using a feather duster which spreads dust around the house I always just use a damp cloth to wipe the dusty surfaces down.
The damp cloth helps to keep the dust from flying through the air and I try to have the windows open as well when I dust to allow the dust to go outside instead of just settling in the air.