Is eating cookie dough without egg safe?
According the the current advice from the FDA, you should not eat raw dough, even if does not contain eggs. Apparently raw flour may contain E. coli.


  People often understand the dangers of eating raw dough due to the
  presence of raw eggs and the associated risk with Salmonella. However,
  consumers should be aware that there are additional risks associated
  with the consumption of raw dough, such as particularly harmful
  strains of E. coli in a product like flour.
  
  “Flour is derived from a grain that comes directly from the field and
  typically is not treated to kill bacteria,” says Leslie Smoot, Ph.D.,
  a senior advisor in FDA’s Office of Food Safety and a specialist in
  the microbiological safety of processed foods. So if an animal heeds
  the call of nature in the field, bacteria from the animal waste could
  contaminate the grain, which is then harvested and milled into flour.
  
  Common “kill steps” applied during food preparation and/or processing
  (so-called because they kill bacteria that cause infections) include
  boiling, baking, roasting, microwaving, and frying. But with raw
  dough, no kill step has been used.


https://www.fda.gov/ForConsumers/ConsumerUpdates/ucm508450.htm