A few thoughts come to mind after reading this email, given the age of this puppy -- that the leakage is from anal gland secretion. Of course, it could be a number of things, even something such as the puppy getting into some sort of oil or other substance. As always, please call your veterinarian if you see anything amiss with your pet.
The anal glands create an oily, malodorous substance that fills the anal sacs, which are positioned between the sphincter muscles of the anus. Dogs may drag their bottom or "scoot" on the floor), lick, or sometimes leak if these sacs become too full.
The anal sacs normally empty with defecation. A softer stool than normal may account for insufficient emptying. Infections and impactions (blockages) are also a possibility.
I am not sure about an "oily smell" described by the viewer. Anal sac secretion is oily; the odor varies, but usually more of a foul, fecal-based scent.
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Related Reading: Anal glands, scooting, impaction and infection of anal sacs
Another possibility, given that this puppy is female, is something called puppy vaginitis. Mild, usually self-limiting vaginal infections are common at this age, and often produce a discharge in the genital area, especially after voiding urine. Other possible signs include licking, scooting, and increased frequency of urination.
Urinary tract infections are common in dogs (and cats) and should also be ruled out at this time.
Finally, puppies being puppies, external sources of an oily substance should also be considered. Check for any chewed containers, trash containers or other possible sources of contamination.
