The most significant step you can take in planning a low-allergen garden is to choose bird- or insect pollinated plants rather than wind-pollinated ones. Plants pollinated by birds and insects produce only small amounts of pollen. Many native trees and shrubs are pollinated by birds and insects.
Lawns can also produce a lot of wind-borne pollen. Choose native species or low-pollinating introduced species such as Greenlees Park couch or buffalo. When mowing a lawn, protect your eyes, nose and mouth with a mask and goggles, or mow while the dew is still on the lawn.
Low-allergy plants include those that are pollinated by insects or birds only, or that are propagated by cuttings or grafting. Some plants you might like to try are:
Grasses and ground covers:
For a full list of suitable low-allergen plants, contact your local nursery or the website of the Asthma Foundation in your state.
This information is from the Yates Garden Guide: fully revised & updated 44th edition, HarperCollins, $39.99. You can have this information and so much more at your fingertips by purchasing the Yates Garden Guide, available at all leading bookstores and Bunnings stores.