Structure of قَرْنَاهَا:
قَرْنَا: subject, nominative with alif because it is dual; also muḍāf.
هَا: attached pronoun, muḍāf ilayh in the genitive position.
The dual nūn is absent because the dual loses its nūn when it becomes a muḍāf.
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Parsing Qarnāhā in Full
Diptote Causes — Compounding and Its Conditions
Structure of قَرْنَاهَا:
قَرْنَا: subject, nominative with alif because it is dual; also muḍāf.
هَا: attached pronoun, muḍāf ilayh in the genitive position.
The dual nūn is absent because the dual loses its nūn when it becomes a muḍāf.