No, you shouldn't be worried.
The lighter any animal is, the less force it experiences when it lands from a fall.
This is because f = ma, as the great vegetarian Isaac Newton worked out, where f is the force the animal's going to experience, a is the acceleration (in this case, deceleration), and m is the mass is the mass of the animal. So if the mass is small then the force is small. Pippa weighs say 1/50 as much as I do, so she experiences 1/50 as much force when she falls.
This applies to any object, animal or inanimate. And in fact it depends not on the total weight but rather on the weight per cross-sectional area. But that's the long answer!
This is just a matter of physics, not biology. It doesn't matter (much) what shape the animal is or even how it lands, except for the unlikely event of the animal landing right on a delicate joint like their neck. I think it's just possible that Pippa may have been winded if she landed right on her tummy, as your dad says. That's unlucky, and may have hurt and annoyed her. But it won't have damaged any internal organs.
This is why even smaller animals like insects can do pretty much anything without getting hurt (unless they get squashed -- that's another type of physical problem altogether). Guinea pigs aren't THAT light, so of course we should try not to drop them, but if we accidentally do drop them then no, we shouldn't worry.
Having said all that, if Pippa's showing any symptoms now, hours later, then of course she should go to the vet. But if she's not showing any symptoms then don't worry at all.