Salticidae
(Jumping Spiders)

Hi, I’m not familiar enough with the species in your region to recognize the exact species. I can however tell that this is a Jumping Spider and none of them are considered to be of medical significance. Everyone’s immune system is different though so of course if you have cause for concern see a doctor. It looks similar enough to Clynotis severus, but I’m not certain. I hope the baby has no ill effects.
http://www.findaspider.org.au/find/spiders/460.htm