It sounds like your paediatrician does not specialise in infant feeding - he doesn't even know the current guidelines. There is absolutely no reason for a bf bub to need a supplement, and in most cases the same is true for a baby starting on solids - especially if they are bfing as well. If you are not going to give your little one meat though, this might be a case where supplements wouldn't hurt unless you make up the iron and zinc levels from other foods. This is something I would talk to a dietician about rather than a paed - they are going to have more specialist knowledge in that area.

FWIW I am not a real fan of supplements. The nutrients in foods are more easily absorbed so a balanced diet is far better at giving you what you need. In the case of iron, the iron in breastmilk and meat is the only iron that is absorbed by the haemo-transporter - all other forms are poorly absorbed and in the case of the iron in rice cereal, less than 5% is absorbed. And if you are getting enough from food than you are basically just weeing the supplements out anyway.