It will be autumn in April. The centre can get cold at night, I've been in Alice Springs in spring when it was in the mid 30's during the day and 2 degrees at night.
Climate averages might be helpful. You can adjust for different months, max and min temps.
Climate and average weather - scroll down to the regions for specific info.
With regard to a coat - the wind chill factor can make it seem colder than it is. You likely won't need a heavy coat, but a jacket (waterproof) will be of use and you can layer if it's cool. It can be wet on the east coast in April. We're suffering from a La Niña weather event, so currently the rain is endless. There's lots of flooding through the eastern states. It's expected to ease by the end of summer but there could still be some rain in April.
You will need a sun hat, sunglasses and 50+ sunscreen. Be diligent about applying it every day, the sun can be brutal, even in winter. The Bureau of Meteorology has a UV index that indicates the risk - today in Melbourne was about 20 degrees, very cloudy and raining on and off all day. The UV index was 8 which is considered a very high risk. Through the areas you'll be travelling at that time of year, the risk will be higher every day.
Sun SafetyYou'll be visiting some beautiful places, I hope you have a fabulous trip.