Yes, that is correct. Pump --> Particulate/moisture trap —> Silica Gel desiccant trap —> Laser. A lot of times you will see the the two traps just connected by a threaded coupler, but you can have hose between them.
If you use an oiled compressor, you need an oil separator in your line. This is always used for painting because oil fouls paint, so an oil separator will be available anywhere airbrush supplies are available. Also, dessicant traps are used in any machine shop because water in the lines kills pneumatic tools; I can’t imagine anywhere where you can get an air compressor that you can’t get both desiccant water traps and oil separators; they are key for normal commercial uses of air compressors.
If you use a silica bead desiccant trap, be aware that you have to recharge the beads by drying them in an oven on low heat regularly. Once they fill up with moisture, they don’t do their job any more.
Putting this all together, buying a diaphragm pump like the one that @NedMan linked to is probably going to be a lot cheaper than outfitting your compressor to work properly with a laser. They are commonly used for aquariums.