Short answer — many brands sold in Australia make cat foods or supplements specifically formulated to support healthy skin and a shiny coat. Common choices (with examples) are:

• Royal Canin — retail “Hair & Skin Care” and a veterinary Skin & Coat diet (veterinary-only dermatology formula with EPA/DHA and linoleic acid). (royalcanin.com)
• Hill’s — Science Diet “Sensitive Stomach & Skin” plus Prescription Diet dermatology formulas (z/d, d/d) designed for food‑sensitivity or skin problems. (hillspet.com.au)
• Purina (Pro Plan) — Pro Plan Sensitive Skin & Stomach and Fussy & Beauty / skin‑support recipes with added omegas. (purina.com.au)
• Advance (Australian brand) — “Sensitive Skin & Digestion” adult cat formulas with skin‑barrier nutrients, zinc and omegas. (floofypets.com.au)
• Ivory Coat (Australian) — fish/salmon recipes promoted for Omega‑3 & 6 to support skin & coat. (ivorycoat.com.au)
• Black Hawk (Australian) — fish/salmon and hairball formulas that highlight fish oil / EPA‑DHA, vitamin E, biotin and zinc for skin and coat. (blackhawkpetcare.com)
• Optimum (supermarket brand available in Australia) — “Skin & Coat” wet pouches and other products with Omega‑6 and zinc. (woononapetfoods.com.au)
• Supplements and toppers (many Australian suppliers) — salmon/fish oil liquids, omegas, and “skin & coat” powdered or chewable supplements (InnoVet, Vetalogica, NAS, etc.) that deliver EPA/DHA, zinc, biotin and vitamin E. (innovet.com.au)

What these formulas/supplements target

• Most skin/coat products add omega‑3 (EPA/DHA) and omega‑6 fatty acids, plus zinc, biotin and vitamin E — nutrients known to help skin barrier, reduce inflammation and improve coat condition. Supplements come as oils, chews or powder toppers; veterinary dermatology diets may also use hydrolysed or limited proteins for food‑sensitivity skin problems. (vetshopaustralia.com.au)

Quick buying notes

• Prescription (veterinary) dermatology diets (e.g., Royal Canin Veterinary Skin & Coat, Hill’s z/d) are typically vet‑only and used for diagnosed skin disease or food allergy. (royalcanin.com)
• If your cat’s skin problem is severe, itchy, bald patches, recurrent ear infections or sudden hair loss, see your vet before changing food or adding supplements — vets can recommend a prescription diet, allergy testing or targeted treatment. (hillspet.com.au)

If you’d like, I can:

• list nearby Australian retailers that stock any of these (pet store / online) or
• give a short comparison (price/available forms / veterinary vs retail) for 3–5 specific products you’re considering.