I have a toddler and a baby on the way (in a few months). Can any other Filipino parents tell me at what age my wife and I can start traveling internationally with our kids?

Your age or the children's? LOL. But I would suggest after your child turned 1 year old so that all the needed vaccines have been completed already. We aren't sure what's really going on in that specific country you are going to unless you really go into detailed research prior to the trip and all we want is our children's safety and also after their protection all the time. Also, by that age his/her immune system is more dependable compared to the earlier months. ANd for your age, no limit at all! As long as you plan ahead, you have fun and enjoy the places with the kids and you make memories together :)

I know some parents who take their kids for a travel even they're only less than a year old. A friend of mine based in Chicago took her kid for a travel to different US states. The kid is just 2 months old. Now that the baby is 10 months old, he has visited the Philippines--lots of cities in and out of Manila! If you really can't help it, then why not? Just make sure you take an extra mile in giving your kid protection. Take immunity shots as possible, give vitamins every day, breastfeed more if your wife is breastfeeding. Keep yourself protected, too! We don't want to get our child infected.