It's a bit of a paradox that in Myanmar, with one of the most rigid and mean-spirited governments in the world, is also for visitors one of the safest from a lack of crime/watching out for your welfare perspective. And the people themselves are lovely and would give you the shirt off their back to help you out. And still a fairly scam-free country, like most of SE Asia was 40-50 years ago.
However, Myanmar's health care system is essentially non-functioning, so you have to take extra care to watch what you eat and drink, not to get injured, take certain precautionary vaccinations, etc. I would personally not feel comfortable taking a child under age 4 or 5 to offbeat or remote locations in Myanmar for this reason, as in the event of an illness, a sick infant/toddler/young child could deteriorate into a dangerous situation before you could get them out and back to good care in Bangkok. Sticking around Yangon-Mandalay-Bagan-Inle main tourist centers is probably OK if you watch a young kid like a hawk. For kids school-age and over, most anywhere Myanmar is fine. They will need to exercise some discipline and common sense...or their parent/guardian will.
Make sure sunscreen and good mosquito repellent (preferably DEET-type) is purchased in advance and taken into Myanmar with you. For all travelers, not just those with kids. Myanmar has the same nasty mosquito-borne diseases as the rest of SE Asia, just much less well-controlled.