I think philh already explained it pretty well. In your question you suppose the laser dot to be 'fairly large', which I think would complicate things (the shape of the dot 'smearing out' as it goes faster). For me, philh's explanation works best if you imagine the laser pointer to be a cannon of photons, emitting one photon after another at a very high rate and in a single direction, with the electrons of the moon's surface always reflecting the photons towards your eye (perhaps a bunch of strategically placed mirrors...).
Actually, the shape of the dot is unchanged by going faster. Since it isn't a real object, it isn't affected by relativistic contraction. If you emit a circle, it'll be a circle.
It is of course changed by what it gets reflected off of, but that's not special to this situation at all. If you're at the center of an enormous hollow sphere and shine an astronomically-bright laser circle around, it'll always be a circle to you no matter how fast you move it.
If the laser emits all photons constituting the dot at the same time, in pulses... I was thinking of the photons that make up the dot arriving at random intervals, but I'm probably making things too complicated.
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I think philh already explained it pretty well. In your question you suppose the laser dot to be 'fairly large', which I think would complicate things (the shape of the dot 'smearing out' as it goes faster). For me, philh's explanation works best if you imagine the laser pointer to be a cannon of photons, emitting one photon after another at a very high rate and in a single direction, with the electrons of the moon's surface always reflecting the photons towards your eye (perhaps a bunch of strategically placed mirrors...).
Actually, the shape of the dot is unchanged by going faster. Since it isn't a real object, it isn't affected by relativistic contraction. If you emit a circle, it'll be a circle.
It is of course changed by what it gets reflected off of, but that's not special to this situation at all. If you're at the center of an enormous hollow sphere and shine an astronomically-bright laser circle around, it'll always be a circle to you no matter how fast you move it.
If the laser emits all photons constituting the dot at the same time, in pulses... I was thinking of the photons that make up the dot arriving at random intervals, but I'm probably making things too complicated.