Cats are prone to spider bites due to their inquisitve nature and and their propensity to get into nooks and crannies under houses and in dark spots where most spiders can be found.
Most spider bites are more painful than they are dangerous. Funnel-webs are not toxic to cats. Red Backs are venomous to cats and may cause the following symptoms:
Ataxia (wobbly gait)
In severe cases it may cause an anaphylactic reaction (difficulty breathing, pale gums, swelling, vomiting and diarrhea, trembling and collapse), this is a medical emergency and needs to be treated by your vet immediately.