Yes, you can immigrate to Australia with family. Applying for permanent residency through the Australian immigration system lets you add your dependent family members. You can include your partner and children who are either younger than 18 years old or older adults who depend on you.
Every family member who obtains a visa will enjoy the equivalent privileges including the ability to reside and work and study in Australia. Through the Family Reunion Program you gain the possibility to sponsor your parents after receiving permanent residency. The application process requires proof of your financial ability to care for dependents along with satisfying all health and character standards.