The first haircut is actually considered as a special milestone that the little one has achieved often varies on his culture and religious. Different countries' babies have different way and some will even accompany by certain ritual and celebrations.
Some babies did their first cut on his first month, some did it when they begins to speak, some had it on his first birthday. It really varies with the tradition of his culture.
Since I'm Chinese, my kids had their first hair cut when they are one month old. I kept a log of his/her hair, tie up with red string and kept it together with his nails and umbilical cord. I placed all of it in a red packet (A red color packet which we use to put money in it and give it to the kids as good wishes during Chinese new year) and slot it beside their baby photo (taken in the hospital on their 1st day to this beautiful world).
The hair cut is done in the morning and celebration follows where all relatives and friends are invited to share our joys and give him their blessings. The father is a good cook and he will prepare a buffet lunch and dinner for all our guests to enjoy. We call this celebration 'Man Yue' which means full month.
Most of my friends did not shave the hair of their babies but some did. Anyway it's your own preference. Some believe that by shaving the hair, you are removing the hair that is growing since they are in their mummy's womb and their hair will become thicker. Well, I didn't do that cos I do not like 'botak' baby hehe....
For friends out there who miss the first hair cut on baby's first month, just do it on a meaningful day. It's the thought that counts.
Cheers to all babies !!!