They are usually quite relax with liquid when you travel with children. So far I have not had any problems bringing more than 100ml of liquid. In fact I carry almost 1 litre of water because I have 2 older kids, and they bring a water bottle each.
There are also hot/cold water dispensers in changi airport's baby room. As for the flight itself, you can get the flight attendant to put mix the water to the right temperature on board.
During take off and landing, remember to either feed your LO some water/milk/latch or some food to created the chewing/swallowing motion to release air pressure from ears.
Enjoy your holidays!
ps : Here are the locations of Changi Airports's baby room
http://www.changiairport.com/en/airport-experience/attractions-and-services/baby-care-room.html
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