We definitely have BnBs here. Just google "bed and breakfast sydney".
As with most large cities, the bulk of accommodation is hotels or serviced apartments simply because the city is more built up. So if she's looking IN Sydney (e.g. the Sydney central area) she's most likely to find lots of hotel style accommodation. (There are boutique hotels and BnBs also though). You're more likely to find more BnBs in the suburbs, rural areas, at the beach etc, which I suspect is true in most places. So if that's what she's after she could try being more specific and searching for a BNB in the specific area she's hoping to stay in.
To me, a BnB is really just a small boutique hotel, or converted house or similar. Still accommodation but a friendlier homestyle vibe. Is that basically what she means?
I'm in Canada, and IME B&B is quite different here as opposed to Great Britain/Europe.
Here, they are fairly high-end places for the most part - down duvets, in-room jacuzzis, en suite bathrooms, breakfast brought to the room etc. They aren't the "budget" type accomodations that you might find in GB - small bedroom, bathroom down the hall, group breakfast served in the dining room. They can be more "destination" places on their own, catering more to a local crowd willing to drive an hour or two. One exception that we found was in Atlantic Canada - there were more "budget" type B&Bs there, but of course there are more larger, older homes than you'd find on the West Coast and these can be easily converted - all those extra rooms.
I don't know whether that's the case in Australia, but it's just a point of awareness. B&B can mean different things to different people.