Hello and welcome!
I don't have anything super specific as far as the actual introduction, but you need to quarantine your new bird a minimum of 30 days in a separate room for the health of your current birds and the new one. During this time, you need to get him to an avian vet for testing. So there shouldn't be an introduction for at least a month. It is important because stress can cause asymptomatic diseases that they can carry to flare up and shed/spread (with or without symptoms). The really important thing, is they can also spread disease without any symptoms (some of which are deadly)--so without testing, even bird from an immaculate breeder in a very clean place could be carriers of certain diseases, as some are spread vertically (mom to baby), as well as through the air etc in the form of feather dust, as well as through contact with food or other contaminated surfaces.
6 weeks is the recommended time-frame but 30 days would be the VERY VERY bare minimum and it is not ideal, nor is it as safe.
see links:
1.
https://www.beautyofbirds.com/quarantine.html
2. some more info:
http://www.beaknwings.org/index.php?option=com_content&view=article&id=289&Itemid=440
3.
http://www.birdvet.com.au/exotics care/birdcare/Quarantine of New Birds.htm
Also, they are both still babies who haven't reached sexual maturity/puberty, so just keep that in mind down the road, as it can and will impact their behavior across the board- including how they interact together. Mustaches generally go through it around 2-3 (but things can kick in a bit before that) and Galahs around 5-6 (but again, the hormones can start before that), so when those hormones do kick in, you will need to keep an extra close eye on them, even if they got along swimmingly as babies, because as they mature, their preferences and attitudes change, so just don't get too lax about their interaction (even if they seem to get along really well)...I would try to train them both now to follow certain structures or routines that may be needed later, even if they seem super-chill for the time being.
