Can there be a planet with no dust?
No, depending on your definition of "dust"
Space is not a sterile vacuum, it is full of stuff ranging from the sub atomic size, to the tremendously huge.
And all this "stuff" is moving, some in a repetitive orderly fashion, and some just blowing around on the cosmic winds.
A planet, by definition, is going to have to be in a system, have an orbit, at least one sun, and be over a certain size, and has to be what ever the term is for "not just a compressed lump of gravel and or ice chunks"
You will not have anything like that, that will not be rained on but tons of material loosely referred to as "Dust"
It does not matter what you work out after the dust has landed, it did land and so the planet has dust, even if the planet is 100% covered in water, it has dust, which before landing on the water was floating in the atmosphere.
The bottom of the ocean is covered in dust, we call it silt.
Having a mechanism to expel the dust is not an absence of dust, just like using some pledge and a rag at your house does not make the house dust free, it just cleans the build up, the dust is still raining down, you will need to dust again.
If you made an artificial planet, dust is still raining down on it.
And even if we allowed it to be called a planet, after totally deviating what defines planet, and put the thing in a static position in deep space near nothing, dust moving through the universe from countless galaxies is still going to find it.
And nearly anything you can think of to build a planet out of eventually becomes dust on it's own.
All things have a finite life before the7 break down.