I and my wife are both diving instructors. We never gave up doing our scuba holidays after we had sons.
Our first scuba diving holidays with a baby was in August 1991, in Sardinia. My son Adriano was 11 months, being born in September 1990.
We went with a couple of friends in a small camping area near the Tavolara island, at Capo Coda Cavallo, renting a "tucul", some sort of bungalow. We did carry a BAT-7 inflatable boat with a 35HP Evinrude engine.
Also the other couple had a baby, one year older than our one (so he did already walk, our one was just crawling towards the water, and of course swimming with his small buoyancy helpers on his arms). Difference was that the wife of my friend is not an instructor, she is just a very relaxed diver, who mostly preferred to stay on the boat whilst I, my wife and our friend (also an instructor) were diving, and keeping care of the two babies. When also she wanted to dive with her husband, we did make two subsequent dives, so the couple staying on the boat did take care of the children.
It was a nice holidays.
The following year we also went to Sardinia, but on the west coast, at Hotel Capo Caccia. The diving center at the hotel was being run by a girl who was a previous student of my wife, named Daniela. She is a PADI instructor.
So we did dive with the inflatable boats of the diving center, typically alternating the one of us who did keep the baby while the other was diving. However at that point our son was almost two years old, he was already swimming very well and snorkeling in the sea without floating devices, and so, with the help of Daniela, we started training him to scuba dive with a small 3-liters pony tank, in the pool of the hotel.
The next years, our son was already using the scuba tank in the pool for the whole year, and when we went again to Capo Caccia, in Sardinia, he was ready to start diving in the sea (of course at minimal depth, 4 meters max).
Since then, our scuba holidays were a mixture of making real dives at the diving center, and these minimal dives with our son.
In 1995 we got a second son, and we started again with the same route.
When both children were already good divers (the older was 10, the younger was 5) we stopped relying on Daniela's diving center at Hotel Capo Caccia, and started again renting an apartment during holidays and using our old Zodiac inflatable. At that point, all our dives were with our children. Typically one of us with one son, while the other parent and son did stay on the boat. Then we did swap. Due to the different age and expertise of our sons, with the older it was possible to make some serious dive, including the caverns of Capo Caccia, whilst the younger was still diving in just a few meter and with no overhead.
I think that time spent underwater with our sons was some of the best time of our life. And, as said, we started very early with both: at 2 years in the swimming pool, at 3 years in the sea.
So good luck with your baby, you will enjoy doing scuba holidays with him: perhaps not the first year, but since the second year he will be happy to be there with you!