I disagree that because we are talking about the Philippines that all of a sudden it is a much more valid concern.
Yes the Phillipines is on the top 10 of nations with rabies. Yes the incidence rate is around 1,000 a year with 300 deaths.
We are talking about a nation of 100 million people though. The statistical chance is even lower when the largest amount of victims to rabies infection are children. You then have to look at the supposed carrier. A puppy of 2 to something weeks old. A puppy of such a young age that somehow got rabies in its small span of life, survived the attack from an animal with rabies somehow, and apparently doesn't have a visible wound. The only alternative would be the pupper getting rabies from saliva exchange with another dog. But that brings us to the biology of the situation. If the dog contracted rabies, the disease would ravage the dog in little to no time. We are talking about a very young puppy, a small body and an incomplete immune system.The dog would be exhibiting extreme behaviors or be dead before OP was outside of the time limit to receive the vaccines.