Yes, there are tiny harnesses - I had one for P-Nut at that age that was adjustable. We got a mesh one at Pet Food Express and the tiniest one came from a dog boutique, I believe. We never, ever let him out front without leash - too many dog nappings around here, plus he loses all semblance of rationality when he sees a squirrel or a bird. He'd jump off a 20 story building to get one!
Btw, I still have P-Nut's first harness. It's sooo tiny and cute, I can't believe it ever fit him