Sounds like a black widow spider.
An entamologist would have to see it to give you an id. Part of it is counting it's eyes.
It is likely a brown widow spider. They're not as venomous as a black widow spider, but you should still be very careful with it.
Information on the medical term for being bit by a black widow spider can be found on WebMD, Medicine Net, Mayo Clinic, Spider Bites, E-Medicine Health, and MedScape.
Spider Creativity, dark powers, dreams, fate, pattern of life, rain bringer, story teller. As the black widow spider is venomous, aggressive and has a reputation as a general and sexual predator you may find these aspects to have upper most in the interpretation.
The spider you are describing is likely the black widow spider. It is known for its shiny black body with a red hourglass-shaped marking on its abdomen. This spider is venomous and can be found in various parts of the world.
This is probably a Red-Backed Jumping Spider. The male has a black body with a bright red abdomen. The female is the same, but the red abdomen has a black stripe. They're found all over the United States. If you want pictures of them, you can find them online at http://kaweahoaks.com/html/spi_phidippus_johnsoni.html.
I've added a link of the life cycle of a black widow spider, hope this helps (see Sources and related links)
You don't have to find the Black Widow. She will find you. (Check the colorful painting.)
There is a spider called a Northern Green Jumping Spider, or Clown Spider (mopsus mormon), with a light green body and red spotted legs. You would most likely find one during the day in Australia. They have excellent vision and it wouldn't be likely for one not to see you sneaking up on it. These spiders actually vary in color. Some have red spots, but some do not. I couldn't find any other spider that matched your description.
Australia
You will receive a key to the Inspector's house, and find the stolen painting there. Then you will also find the Black Widow...