If you don't have software that lets you clone from one plate to another, you can achieve the same thing in a more "manual" way using Motion.
Take the clip into Motion and duplicate it so you have two layers. Drop the opacity of the top layer down so you can see through it - like an onion skin. Then position the top layer in such a way that a clean sample of color, matching where the dust spot is, is directly over the spot. Ideally, if there is camera movement, you want to find a sample that is located perpendicular to the movement of the camera. So if the camera is panning left and right, look for a solution above or below the spot. The closer your sample is to the spot, the easier your job may be.
Then build a tiny matte that's barely bigger than the spot, and add a little feather to your taste. That matte is for the top layer, so only the little bit of texture covering the spot is being applied.
Now increase the opacity of the top layer to 100% and see how it looks.
If there's a slight color shift, you can add some color correction to that top layer, or you can even try dropping the opacity a little. This will be something you may need to play with if there is a gradient falling across the footage where the spot is.
This will at least get you started - without having access to any cloning tools. And because it is sensor dust, you won't have to track anything, so that part is simple. The feathering on the matte is important so that as the camera pans the scene, the new texture being applied over the spot will slide in and out without drawing too much attention. Depending on camera movement, you may need to work with a new layer everytime the camera moves in a new direction - or if the subject suddenly changes direction. Just dissolve from one layer to another to help with the transition, and you should be able to hide it.
If it sounds like a lot of work, don't be too disappointed. Dust-busting and wire-removal are valuable skills.
PS I just found this link where someone demonstrates the same principle, along with motion tracking, for Motion. Picture's worth a thousand words.
