You may find this list of (local-ish) plant nurseries useful. Be aware that many of the nurseries below were set up to preserve and propagate plant species endemic to their local areas. There is as yet no nursery dedicated specifically to plants indigenous and endemic to Stonnington.
VINC (Victorian Indigenous Nurseries Co-op) Yarra Bend Road, Fairfield, VIC 3078
Bili Nursery and Landcare 525 Williamstown Rd, Port Melbourne VIC 3207
Greenlink Box Hill 41 Wimmera St, Box Hill North VIC 3129
Bungalook Nursery 63-107 Fulton Road, Blackburn South, Vic 3130
CRISP Indigenous Plant Nursery 17 Greenwood Avenue Ringwood, VIC 3134
Operation Revegetation Pty Ltd 72 Scoresby Rd, Bayswater VIC 3153
Greenlink Sandbelt 587 Heatherton Rd, Clayton South
La Trobe University Bundoora (also nesting boxes)
Melton Botanic Garden 40 Lakewood Blvd, Melton VIC 3337
Kuranga Native Nursery is a commercial outfit (nb: ‘native’ plants are not necessarily indigenous!) but has an extensive range and helpful staff – 118 York Rd Mt Evelyn, VIC 3796