My understanding is that Indonesia hasn't asked for international assistance at this time, or if it has it has done so basically this morning. So it is a bit wait and see, unlike the other pacific countries Indonesia does have significant capabilities in this area, its just it takes some time to organise and mobilize them, just as it does with international aid.
“We have learned our lesson from the Aceh tsunami in 2004 that, regarding international help, we have to be selective and only accept aid that we actually need,” BNPB spokesman Sutopo Purwo Nugroho said at a news conference. “We need to select the countries based on their capacity to help us.”
Indonesia open to overseas aid after earthquakes, tsunami
Australia would be quite keen to assist, so in the next week or so I wouldn't be surprised if the C17's and an amphibious ship are both mobilised.
The LHD I think would be ideal, as it can bring in heavy machinery, and fuel, water and people, and not add a burden to the local area. I wouldn't be suprised to see them hang around for an extended role.
The near by airport was apparently badly damaged with an ATC killed and large cracks in the runway.
Its these kind of events that I hope our efforts with the US and China and Indonesia in inter-operation are useful.