Ayush homam can be performed,every annual bith day upto 5 years or even more according to resources and facilites.Ayush Homam normally requiers 4 purohits or 1 purohit and 3 modestly informed brahmins or even 3 family elderly members can do.--Afterwards Nakshttira Homam can be performed,till 16 years.My mother performed nakshattira homam for me ,till i was around 16.Nakshattira Homam requires only one Purohit.
Ear piercing(karna vedhanam) one has to consult an expert Purohit.I think Karna vedhanam,Shouram and all can be done only if the age is odd or even number-there is a rule governing these Sanskarams in Sathapatha Braahmanam
I think Nothing wrong in celebrating Ayush Homam on the next (2 nd) year.The very same experience ,experienced by me in my life also.
My daughter S.Varalakshmi (now she is 18),First Birth day falls on Solar Eclipse on Dec/91.
Then I consulted Vadhiyar and celebrated the ear boring function on the next Janma Nakshatra and accordingly I celebrated her First Birth Day and ear boring ceremony only on the 13 th month instead of 12th month Jan 10 th 1992 instead of Dec/91.