What kind of spider is this from Sydney, Australia?
Good news is that this is definitely not a funnel web spider (Atracinae), which, by the way, is not that dangerous&#10043;. 

The image doesn't have a good resolution, but that seems to be a spider from the Family Lycosidae, known as wolf spiders, more specifically Venatrix pictiventris.

Here is an image for comparisson:



Source: http://www.findaspider.org.au/find/spiders/497.htm

This is the distribution of Venatrix pictiventris in Australia, going from Tasmania to Queensland, with most observations in New South Wales:



&#10043; I advocate for the protection of sharks, spiders, snakes, bats etc. So, whenever I can, I try to demystify arachnophobia. People love saying that the funnel web is deadly and so on, but for you to have a better idea, moths (e.g. Lonomia) kill more people than spiders.