Bolognese would be legal in Australia - they're not like pitbulls. But I don't think anyone has any in Australia - to import a breeding quality dog would cost in the order of $20,000 by the time you've bought a nice one, and you'd probably have to go to Europe to find it - and follow all the recommendations about research and meeting the parent dogs, air fares to get it back, and then it spends between one and three months in quarantine when you get it here - and you get to pay for that and it's not as cheap as regular boarding... and you probably wouldn't want to do that to a puppy.
Chances are anyone offering to sell you one of these in Australia - may be an overseas scammer - so I'd put the Bolognese in the too hard basket myself.
The Bichon is a very laid back dog, the one I know manages a couple of laps of our local oval (about 600m per lap), he lives with a couple of Lhasa apso crosses, who are much more energetic. All of those are very affectionate with their owners, and less so with strangers or even other friends (like me), not like some of their buddies who are all over me any time and all the time. (I have treats and magic ear rub fingers).
I don't think the coat is a lot of work - I know they all get clipped about once every 6 weeks, and I'm not sure they get bathed more often than that and not sure how often they get brushed. I brush my cattle dog x about once a week thoroughly and more often if she's shedding a lot (happens when the seasons change). Just as needed.
If you want a dog glued to the back of your knee - the cattle dog is it. And the cattle dog will be very protective - which you may or may not want. Great for repelling door to door sales - but a donotknock.org.au sticker might be more polite.
Poodles - apart from the regular clip - are pretty easy too. But they're much more energetic and demanding of your attention than the Bichon. They are related to working dogs - so they like to have a job to do and they're frequently smarter than their owners, really good owner trainers. I wouldn't say that about the Bichon I know or his Lhasa friends. Not the brightest dogs I've ever met.
If there is something exciting next door (like a blue tongue lizard) - the Lhasa will bark relentlessly but the bichon does not. The poodle - it will depend on how you have trained it.
Best way to find out what these dogs are really like (since grevillia and my experiences of them have been very different), is to meet some and their breeders at some dog shows.