I just got the home return permit for my 2.5 mth baby girl. Her Dad is a Chinese national with HKID (i.e. no permanent residence), I am Canadian by birth but have HK permanent residence. My HKID and home return permit (I already had it) was enough to get her the home return permit.
Carang and JoTs are right, you need to get the HKID/HKSAR Passport first, which your daughter is eligible for if she was born in HK and is Chinese.
Assuming you can get her HKSAR passport/HKID, visit any CITS branch (I went to Tsuen Wan) early when it opens to get a number. It can get really busy depending on the day and branch, so I suggest going early. You must bring her with you. She can be asleep, they just check quickly vs. the photo.
We paid $460 for her HRP, which included an extra $200 to get it in 5 working days, instead of 12.
Photos - their website gives the specifications, but the lady who processed our application just took the two we gave her - which were from her HKSAR passport/HKID application. 90% of the application must be completed in Chinese. Here's the link to the application. Bring her birth cert as well.
http://www.ctshk.com/zhengjian/02.pdf
If you can get someone to read Chinese, here's the official CITS link. Good luck!!
http://www.ctshk.com/zhengjian/gangao.htm#requestnk for info.