Grasses such as cooch and wintergreen suffer more from dogs doing their business on the lawn. A more drought tolerant, hardy turf/ grass for the Brisbane area is Buffalo palmetto and this will be a harder grass for him to dig holes in.
Have your landscape design incorporate a toilet area where he gets trained to use this area only. This area can be gravel or sandpit in the far corner tucked away near a lined rubbish tin with a pooper scooper handy. Possibly bordered with some scented plants such as Jasmine, Rosemary, Lavender or Daphne to help disguise the unpleasants.
Some plants could be a high risk to an excited dog such as Yucca, Dracena or Phoenix palms for example as they their spiky leaves could damage your pets eyes. Also cactus gardens could pose a similar threat. Log into www.aspca.com to find poisonous plants for dogs so you know what species to avoid in your garden.
Avoid spraying toxic chemicals where your dog could be roaming, or where it could land in his water bowl which may be your water feature. Don't plant fragile plants around the boundary if your pet likes to patrol the boundary fence when strangers pass by. You may have to create barriers with timber garden sleepers to avoid him trampling your precious plants in certain areas.
If he digs holes trying to escape under the boundary fence then a concrete border could be constructed underneath the fenceline to avoid this.
If he digs holes in your mulches you may have to use a heavier mulch like brown pebbles or 100 mil rocks but remember he will need some grass to call his own.