What we carry is different to most (both Jase n I are level 2 Ambulance officers with ST John Ambulance here & Jason is an Industral Medic) so we dont have a typical kit.. ours is more of a trauma / emergency response kit
but a thing to make sure of is that you dont get led into buying more stuff than you need or can use.
Most places that do snr first aid will also give you basic courses in remote first aid,child first aid etc, so its always worthwhile to look into that. As horrible as it is & you may never need it but a course in basic resuscitation for children & babies is always money well spent.
A normal basic off road first aid kit , with a few extras, such as a thermometer,baby panadol is probably the main things to have. One of our ruggies is Asthmatic so we carry salbutamol (ventolin puffer) and a space chamber with a mask attached as well. As your kids get older you can get other paracetamols & medications but there isnt much you can buy for the real littlies..
With a sick baby the hardest thing to regulate if you dont monitor it is their temperature a cheesecloth blanket dampened with water & rungout is great to pat down with to help cool a fever BUT dont do the old submerse in ice water as that is no longer recommended. (We had one lot up here stick a feverish baby in an esky full of icewater
it bought the temp down alright.... but then it was the opposite..
Just making sure you know where you are & what the capabilities are of yourselves to act in an emergency & how to get to help if you need it are the best things too.
Jacq