Arachnophobia

I know spiders are our friends. They eat insects and are generally helpful critters. I know this and tell this to our three year old daughter, allowing her to extrapolate even more friendly characteristics from "Charlotte's Web". But make no mistake...spiders are not my personal friends. While I can appreciate them from a distance, I want them nowhere near my body. Ever. And now we live in Australia, where there is one particular deadly spider to be avoided: the redback. Related to the black widow, they are jet black with the tell-tale red marking on their topsides. Of course, the locals think I'm crazy for being worried, but I'm new here and these things make me nervous. I have researched them and learned that they are just about impossible to get rid of (they can close off their lungs for up to 7 hours if you spray!), but thankfully are rarely found in houses. The bites are nasty for adults but deadly for young children (of which we have two!), so I am very redback averse. And there are currently two unidentified black spiders in our house. One of them is quite small (a juvenile?) and the other is HUGE (the size of an Australian 50 cent piece, which is huge in my eyes when it's in my house). I just found the latter about an hour ago, and I'm still quaking about it. It's in the kitchen skylight, and it has a hiding place where the wall doesn't completely meet the ceiling right at the top. Lacking spray, I tried to suck it up in the vacuum, and it just laughed at me. It was too strong to get sucked away. This does not make me feel better about it, believe me. The hardest part for me right now is not being sure what type of spider it is. I only saw it from underneath, so I couldn't see if it has a red back or not. It could be the Black House Spider (which eats redbacks!), but those have nasty bites too. I want it gone. But I think it has other plans. For now, I just hope those plans include staying where it is to patrol the skylight with impunity.
Please cross your fingers that it doesn't come out to get me for the whole vacuum cleaner episode.