Which printer for non-visible dots (dpi)?

[Ginger]

I am wanting to print water slide decals for nail art. However, when I print, the graphics are made up of little visible dots. Which I totally understand for raster images (I used to use Photoshop). But, I thought that using vector graphics in Illustrator, it would eliminate these little dots that are printed. I thought that they would print as solid color graphics.

Here is more:

• I already have the water slide paper (not part of the issue, I'm sure).
• I have vector art and I use Illustrator to create/edit my decals.
• I own a Brother laser printer (MFC-9130CW) and I set it to 1200 dpi in the print settings window.

Do I need a new printer? Do I need to adjust settings somewhere in Illustrator or in the Brother's print settings?

Thank you all in advance, for your help!