What does the Pip pet do?

It helpes the room where dweller with Pip is stationed to achieve the objectives faster.

For instance, if you have objective extinguish six fires, you'll only have to deal with two fires in that room. Same works for other objectives.

If you have objective that says collect X resources each resource collection from the room with that pet inside is multiplied by that amount too.

Needless to say it's very useful in completing hard objectives, like killing Deathclaws some amount of time, etc. etc.

UPD: I can confirm this, as I have the German shepherd, which also improves the objective completion rate.