The assumption is the first problem, no? If the formal language is complete, it must be inconsistent. If it is consistent, it must be incomplete. If the language is incomplete or inconsistent, you may be unable to encode dog behavior in it.
What about describing an electrical circuit formally? Surely this was thought possible before Principia was published.
The “something” Gödels proof talks about is axiomatic systems. It doesn’t talk about physical objects.
Even the full formalization of mathematics wasn't considered certain (*) before Hilbert/Principia and those 20th century attempts. Much less the formalization being applied everything in the physical world or even animal behavior.
* in retrospect rightly so, because it wasn't, at least not without inconsistency/incompleteness.