qset = (
    Q(name=searched_name) &
    Q(birthdate=searchet_birthdate) &
    ..etc
)
Person.objects.filter(qset)

# BUT I DONT WANT TO ADD CERTAIN Q(..) to qset if searchet_XXX is empty string

# like for ex. searched_name = '' then just this

qset = (
    Q(birthdate=searchet_birthdate) &
    ..etc
)
Person.objects.filter(qset)