https://www.experienceperth.com/article/wed-03212018-1630/best-places-spot-dolphins
Apart from going to Mandurah and Rockingham, you may be lucky enough to encounter/ spot wild dolphin in Perth itself (Swan River).
The best time for dolphin watching in Perth is between September and May.
The spots / locations include:
Blackwall Reach @ Point Walter, a pretty stretch of foreshore with a sand spit, where you can also see waterbirds feeding and resting and relax in the café.
The Narrows Bridge has the benefit of creating a natural funnel, which gives dolphins an opportunity to find a lot of fish in a small area. Look for them between here and Matilda Bay, and in the wake of the ferries. Combine your dolphin watching trip with a visit to beautiful Kings Park.
Deepwater Point is another section that forces fish into a deep spot, ideal for dolphin feeding. Take a picnic or visit Deep Water Point Café, go for a swim or walk along the foreshore, visit Heathcote Reserve for refreshing river views, and look out for sea birds too.
Also off the coast near Ocean Reef and Sorrento.