After A Woman Receives The Gardasil Vaccine How Soon After Can She Safely Have Sex While Benefitting From The Vaccine?

With most vaccines the body achieve full immunity within days, but I can't get specific data about this one.

Gardasil is a proprietary name for a vaccine against some varieties of the human papillomavirus (HPV).  These 4 strains of HPV cause the majority (~70% of all cervical cancers).  Gardasil is typically administered in 3 phases, to achieve a 95% chance of immunity.  So the level of protection depends more on whether a person has had all 3 jabs, yet. 5% of people getting all 3 jabs still won't have protection, and all women are still vulnerable to the remaining 70+ types of HPV that cause the other 30% of cervical cancers.  The usual safe-sex measures, like barrier methods, should still be used whenever possible.  

Most of the monitoring to figure out how good the vaccine is, has been done from about 6 months after the first vaccine jab was given.  So it's hard to give a more specific point when it starts to help out.