The answe to this question can be found in Chapter Eight of this novel. In this section, Hester finds herself being forced to fight to keep her daughter, as those in power believe that she might not be best suited to bring up her daughter because of her sin and her status as an outcast. When Hester tries to state her case, she reveals her obvious love of Pearl and then appeals to Dimmesdale to support her. He responds with the following words:
There is truth... in what Hester days, and in the feeling which inspires her! God gave her the child, and gave her, too, an instinctive knowledge of its nature and requirements--both seemingly so peculiar--which no other mortal being can possess. And, moreover, is there not a quality of awful sacredness in the relation between this mother and this child?
Dimmesdale thus argues that Hester should be able to keep Pearl because of the link and intimacy that there is between them. He also identifies an "awful sacredness" in the relationship between Pearl and Hester, which again indicates that Hester is the person best suited to look after Pearl.