Well, I haven't had to deal with this, but I just wanted to agree with what Ambah said regarding the buses.

I don't know what things are like in Sydney but DH and I lived in Brisbane for quite a while and didn't have a car so we used public transport all the time. We often noticed how difficult it was for one person to get bubs & a pram on and off the bus, especially since a lot of the time they'd also have shopping bags to deal with as well. Some bus drivers even got very narky about the amount of time it took. We often had to help mums with prams get everything on board. One time DH even had to help an elderly lady with her stuff because when the lady asked the bus driver to help her he refused saying he wasn't allowed to due to some kind of safety regulation.

Good luck!