If your friend has convictions these will have to be declared and she will need to apply for a visitors visa rather than an electronic travel authority ( eta). If she arrives in Australia with an eta and her convictions are then discovered by immigration she may be refused entry since she will not be in possession of the correct type of visa.
My understanding is that the australian authorities' decision regarding the granting of a visa will depend on how seriously the convictions are viewed and whether she is deemed to present a potential risk to australian citizens.