Large language models (LLMs) are widely used as general-purpose knowledge sources, but they rely on parametric knowledge, limiting explainability and trustworthiness. In task-oriented dialogue (TOD) systems, this separation is explicit, using an external database structured by an explicit ontology to ensure explainability and controllability. However, building such ontologies requires manual labels or supervised training. We introduce TeQoDO: a Text-to-SQL task-oriented Dialogue Ontology construction method. Here, an LLM autonomously builds a TOD ontology from scratch using only its inherent SQL programming capabilities combined with concepts from modular TOD systems provided in the prompt. We show that TeQoDO outperforms transfer learning approaches, and its constructed ontology is competitive on a downstream dialogue state tracking task. Ablation studies demonstrate the key role of modular TOD system concepts. TeQoDO also scales to allow construction of much larger ontologies, which we investigate on a Wikipedia and arXiv dataset. We view this as a step towards broader application of ontologies.