Of the countries you mention the best trekking is, IMO, in Northern Thailand. This is essentially jungle/hill walking in a fairly mild climate. Visits to hill tribe villages and elephant farms are usual. The treks can be physically demanding but are not beyond a normally fit and active person. They have a strong cultural interest. Jan/Feb is a good time to go as it is the dry season. For some typical walks and some good advice on equipment see, for example: http://www.thailandtravelplan.co.uk/trekking-thailand.htm
In Vietnam the only trekking I have done was around Bac Ha. It is similar to Northern Thailand but perhaps a bit more physical. See, for example: http://bachatourist.com/bac-ha-tour/56-muong-khuong-bac-ha-special-trek.html
There are also shorter walks around town.
I have never been to Cambodia.
If you are able to get to Lombok, the island east of Bali, there is a great trek up Rinjani, a high volcano. It takes three to four days and is, IMO, one of the best treks in SEA. However you may be a little early for the best weather. See, for example: http://www.trekkingrinjani.com/
You will not need much equipment for these treks. See the links for some details. I suggest that you visit Mountain Designs in Perth and ask for some advice. They are a reputable company and I use use them here in Sydney.
Unfortunately I do not know anything about walks in WA! The people at Mountain Designs will be able to help.