Some dogs never do it, so it's not an age thing. I see it more as a management thing.
I think the most important thing you can do is work to keep the puppy calm and build up her confidence. One thing that will help is being careful what tone of voice you use. Instead of a high-pitched, squeaky voice, pitch your voice lower and speak softly. Also avoid direct eye contact and don't "hype" the puppy into a frenzy. Sit down and let the puppy approach you at her own pace. Chuck her gently under the chin rather than patting (thumping!) on the head. Stroke gently from front to back rather than scrubbing and thumping the dog on the ribs. Everything should be calculated to keep the puppy calm and quiet. I've given this advice to many clients with piddling puppies, and have received positive feedback that these techniques work wonders. Caveat: everyone in the family, and anyone who handles the puppy, must do these things. Given time, the puppy develops confidence and the piddling stops. Basically, the puppy is just over-stimulated, overwhelmed, and loses control. Good luck!