Is this rosacea, eczema, perioral dermatitis or something else? (Photo)

It is difficult from the photos to tell exactly what is going on and it is important to see a dermatologist as you are going to do. in the meantime, use very mild products such as Cetaphil cleanser and moisturizer and a daily sunscreen. Since you are in Australia use SPF 50 every morning

Very hard to see given the photos. A general dermatologist can go through a history- f history of rosacea, eczema, atopy. Close examination can exclude comedomal acne, or even hormonal acne. Additionally patch testing can exclude irritant or allergic contact dermatitis. Once these cause are excluded, and traditional or conventional treatments are used, your rash may settle. If not, lasers can help. Video below explains how I use lasers to treat rosacea and facial redness. All the best, Dr Davin Lim. Brisbane.Australia.