We've travelled through Cambodia twice with our kids in the last few years - their grandmother works there. Last time they were 10, 8, 6, 2 yrs and a nine month old. Khmers are very kind and tolerant with children and the country is increasingly easy to travel around (when we went first in 2000 pre-kids it was very different from now).
We always stay in 5* hotels/aparthotels and take great care with food when travelling - only freshly cooked in front of you, nothing that may have been stored. We've never had any tummy upset with any child and have travelled around quite a bit although not to the remotest provinces. Some guest houses do have bed bugs, cockroaches, major mossie infestations so I would always save up for good hotels - tripadvisor is a good help.
January is a great time to go as it's just settling nicely into the dry season but before the heat really builds up so good for little children. It's also not dengue season (daytime mossies) so although you need to avoid the children being bitten in the evening, it's not a 24/7 problem which some months can be. We have always covered the children up in the evenings and, in Phnom Penh, stayed by the river where there's more breeze to keep the mossies from landing/biting - not one bite on any of the five kids last time we went over the three weeks ....
Phnom Penh and Siem Reap have biggish supermarkets and department stores where you could stock up on nappies etc if you still need them, and when I travelled with babies, I always took a large plastic bowl and sterilising tablets, several plastic spoons, sippy cups etc and just sterilised them regularly as we travelled.
There are good health clinics in Phnom Penh and Siem Reap but all expats have any major treatment eg cancer in Bangkok. Land mines are well cleared from anywhere you're likely to be going but if you do go in the jungle, stick on well-trodden paths....
Have a great time - it's a fabulous country to visit, our kids have nothing but the happiest memories from travelling there and you may find, like mine, that they don't really want to return to UK ever again ...!