Do NOT let your puppy out at 10 weeks, especially not in places where she can be in contact with other dogs.
There is NO WAY a puppy is fully vaccinated so young... My vet said they need a booster at 16 weeks, some say 12 weeks, but either way, 10 weeks is way too young, they are still under their mom's immunization at this age and thevaccines probably did nothing... so as soon as the immunization wears out, she WILL catch something if she's exposed to it.
I would get another vet, if yours really told you that the last injection is at 10 weeks.