Words for “water” and “mother” seem to be close across languages, but I don’t see how “dog” makes that category.
Supposing there was some sort of prehistoric universal language it's going to be difficult to identify since every language seems to have sounds that aren't found in others. The "L" sound in English can't even be heard as different from "R" to Japanese speakers. And Japanese goes further off track with "Ha-ha" for mother and "Chi-chi" for father. Then there's that guttural sound in Arabic which resembles somebody choking on a peach pit represented by a letter called "ein" (say that while swallowing and you might come close). And we mustn't forget the clicking sound in Xosa.
All in all, then, figuring out what people were speaking at the base floor of the Tower of Babel isn't going to be easy, facile, kantan, leicht, kal, or baseet.