I think there is an interesting economic question buried underneath your post, although I would be careful about drawing historical conclusions from what seems intuitively obvious. Many of the claims about the sequence of writing, language, governance, and mathematics are ultimately empirical questions that archaeology, anthropology, linguistics, and cognitive science continue to investigate.
That said, one aspect of your argument resonates with a behavioral-economic framework I have been developing, the Productive Value-Productive Power (PV-PP) framework.
One of the framework’s assumptions is that economics should not begin with money, markets, or even governments. It begins with exchange. More specifically, it begins with exchanges that increase or decrease the future productive capacity of the participants.
Viewed that way, information is not merely something that affects markets through information asymmetry. Information is itself a productive asset that can be exchanged. Teaching another person where water can be found, how to make a tool, how to recognize poisonous plants, or how to cooperate during a hunt all increase the recipient’s future productive capacity. Those exchanges are economically meaningful even though no money changes hands.
From that perspective, I suspect the earliest human “economy” consisted primarily of repeated exchanges of goods, services, skills, and information within small groups. Formal institutions such as money, contracts, taxation, and governments would have emerged much later as mechanisms for organizing increasingly complex exchanges rather than as the origin of economic behavior itself.
Regarding the duck example, I think it illustrates something slightly different. A duck recognizing that one duckling is missing demonstrates information processing and environmental awareness. Whether that should be described as economic reasoning is a separate question. Economic behavior generally begins when an organism changes its actions based on expected future outcomes and exchanges resources, effort, or information with others.
In short, I agree with the broader intuition that information is more fundamental than many economic models explicitly acknowledge. Where I would be more cautious is in inferring the historical order in which language, writing, mathematics, governance, and other institutions necessarily evolved. Those are fascinating questions, but they require evidence beyond what appears logically obvious.