hi......
i actually work for virgin at melb airport....
i cant really say much except that we do have a few strollers that float around occasionally that you can use.in saying that they are often being used.....we can offer these so you can check your pram in at the checkin counters.....
and we are more than happy for you to take your own pram to boarding gates....it can only be a single pram you can not take a double pram down as they are to big nd bulky for the pit crew guys to carry up and down the stairs.....when you checkin your pram u need to be at the gate 30 mins prior to dep so we have time to organise the tags and the guys to oick it up to make sure it gets listed and gets on the aircraft
we do a pre boarding announcement for ppl who require extra time to board(old ppl ppl with crutches etc) and ppl travelling with infants or to age of 5 to board first......
i have travelled on the bus(its orange cant remeber the name of the company) and it was very easy mind u i dont have a baby yet but i would still do that evn if i had a baby.....
i often see our cabin crew walking up and down the aisles with a baby on their hip while we finish boarding and have seen it several times in flight....which im sure would be a nice break for mums and dads!!!!
i cant say much about tiger have never flown with them but get HEAPS of really bad reports they only have a 15kg weight limit also....
same with jetstar..i have flown with them but with no baby but found all their crew to be decent...

hope it helps