Sorry, Tammie. That's all I could tell you. Because I'm not a HK citizen, I have to go to HK Immigration office for a lot of things: my ID, baby's ID&passport, etc. so everything kinda mixed into one.
Since you have a small baby, I suggest maybe your husband can go to HK Immigration office and ask them. He can take the forms you needed, too, and you can fill them at home. They have the forms in English. Make sure that you take all the forms you needed, so you don't have to go there again.
If I'm not wrong, you can apply for ID&passport together. Then you can mail the application forms, together with your baby's passport pictures (you can take your baby to any picture shops and have them take his picture, passport size), and cheque. You also have to choose where you want to take the ID&passport (first choice, second choice...). When they're ready, they'll send you a letter saying that you can pick the ID&passport in.... Then you have to bring your baby. And if the baby cannot go, if think you have to bring some identification, or...well, ask your husband to ask them when he's in Wan Chai.
Really sorry, I just wish I could give more information.
(btw, I applied the ID&passport for my baby when he was 5 months old, around March last year)