Is it permissible to supplicate for marriage to a doctor specifically, knowing that this is a wish and desire for the divorced woman?

It is permissible for a Muslim to ask Allah Almighty for everything they desire and need, as long as it is not a sin or a severance of kinship ties. This is based on the Almighty’s saying: "And your Lord says, 'Call upon Me; I will respond to you,'" and the Prophet, peace and blessings be upon him, said: "The supplication of any one of you will be answered as long as he does not supplicate for a sin or the severance of kinship ties." Therefore, there is no objection for a divorced woman to ask Allah Almighty for a righteous husband according to what she wishes. It is better for her to ask Allah to ordain what is good for her, grant her a righteous husband, and make her content with what He has decreed for her.