Radiation is all around us, all the time. In fact, you receive more radiation from eating a banana than living near a nuclear plant for a year. Other normal activities such flying, x rays and CT scans have a significantly higher radiation dose.
No energy system has a perfect safety record, but nuclear is statistically just as safe as solar panels and wind turbines and far safer than fossil fuels. In fact, nuclear is estimated to have saved over 1.84 million lives worldwide by replacing fossil fuels.
In over 20,000 years of combined reactor years of operation there have been 3 major accidents: Three Mile Island, Fukushima and Chernobyl. Chernobyl was the only accident leading to deaths from radiation. It occurred as a result of poor management practices and an outdated reactor design.
No nuclear reactor built in the past 40 years has had a major accident. Advanced reactor designs include passive safety systems which work without the need for human intervention or backup power. Some designs using different coolants promise further safety benefits. For instance, China recently started operating a meltdown-proof reactor.
Nuclear plants are built to be secure for any potential threat. In addition to the use of highly trained security guards, nuclear facilities are built from the ground up with security in mind.
For instance, nuclear containment structures are usually over a meter thick composed of steel reinforced concrete built to withstand the impact of an A380. Nuclear plants are also designed to manage modern threats such as cyber attacks with highly advanced cyber security systems.
The peaceful applications of nuclear science and technology including nuclear power does not mean nuclear weapons. Nuclear power plants typically use uranium enriched to 3-20% compared to nuclear weapons which require uranium enriched to 90%. Moreover, there are strong regulatory frameworks governed by ANSO and the International Atomic Energy Agency to ensure proliferation does not occur. As a member of the non proliferation agreement, Australia would is legally not permitted to produce nuclear weapons.