Australian White Tailed Spider in my house

Yesterday:

Just as I thought my "Widow" is looking hungry... She isn't as fat as she was before. I planned to catch another spider for her.

This morning:

At 6am in the morning while going for number 1, I saw a spider (size: approximately 18mm) in the cat litter box.
Didn't think it was great to leave it there where the cats will be scratching...so I sacrificed my "Widow" chopsticks... grabbed the spider... tossed it into my Widow's play pen.
I looked closer to identify what spider it is... Perhaps a House spider?


FFS... I just sent my Widow to hell. It's an Australian White Tailed Spider. To be honest, I do not know who will die of whose venomous bite. As for us humans, Australian Redback Spider's (also known as the Black Widow) bites are dangerous but there is antidote for those who are bitten.
White tailed spiders... unfortunate to us in Australia, are one of those which we DO NOT HAVE ANTIDOTE.

This is what I've researched so far:

Habitat and Biology [Link]

Webs consist of a tangled, funnel-like upper retreat area from which vertical, sticky catching threads run to ground attachments. The Redback Spider favours proximity to human habitation, with webs being built in dry, sheltered sites, such as among rocks, in logs, shrubs, junk-piles, sheds, or toilets. Redback Spiders are less common in winter months. Daddy-long-legs Spiders and White-tailed Spiders are known to catch and kill Redback Spiders.

She is dooooomed!
Who do you think will win? I would have just died if I weren't careful. Sheesh...

=/