You need to have this cat examined by a veterinarian. When you go to your appointment bring in a fresh stool sample, hopefully one that contains these white dots. Your veterinarian will want to run fecal tests to screen for intestinal parasites, giardia, and look for bacterial overgrowth. The most common worms seen in the stool are roundworms (look like white spaghetti) and tapeworms (look like white grains of rice). What you are describing does not sound like either of these.
Also screen your cat's environment to see if there is anything that fits this description she may be eating.
Also screen your cat's environment to see if there is anything that fits this description she may be eating.