I highly recommend Fortitude Canine with Algal DHA. I have been giving this to my growing pup and I have seen an improvement in his health and coating. Its a natural food suplement for dogs and includes omega 3 fatty acids. You can find it at Kauffmans Animal Health and
order it directly online.
http://www.ka-hi.com/
Unless your little boy has specific problems of any kind (apart from the sensitive stomach) at 1 year old, I would just make sure he gets a healthy, balanced diet (for a dog's requirements) no table food, not even a little bit, and he should be fine on that.
I know some people think a dog should have supplements all over the place from the beginning, but that's not my opinion. (And that IS only my opinion, so if you disagree, I understand)
I believe in using supplements when needed. A pro-biotic, for example is very good support after any antibiotic treatments, or if there are specific digestive disturbances.
But a dog will get all the vitamin/mineral/essential fatty acids etc from his food, as long as a really high quality food is given, which suits him.
A GOOD food, plus water, and the occasional healthy treat, are all the food requirements a dog needs to stay fit.
Of course, if he does begin to develop arthritis, or even if there is the threat of it (for example, after any injury) -then you could start him on a Glucosmaine/Chondroitin supplement. I am unsure of the dosage for a tiny thing like a Yorkie. You would be best to ask your vet for advice.
It would be different if he had some health condition, or vitamin deficiency, in which case he would need supplements. Then that would be prescribed by your vet.