In Smt. Farzanabai v. Ayub Dadamiya; AIR 1989 Bom. 357 the Bombay high court observed that under Guardians and Wards Act, the personal law of the parties is a factor which is to be kept in mind by the court subject to the interest of the minor:-

"Guardianship of a person in relation to a child belongs primarily to its father, the mother's being only a pre-emptive right to keep the father away for a legally prescribed period only from a particular aspect of the guardianship of person, namely, the custody and physical upbringing of the child''.

It may be said, therefore, that mother has a right to the custody of her child for some time, because except her, no one can handle and nurse a child during its infancy. But her custody of the child is subject to the supervision of the father who, as a legal guardian, is under an obligation to provide means for the upbringing of child.

2) apply for guardianship of child after divorce 

Guardianship is granted only after divorce between couple. Without divorce there is no question of exclusive guardianship. Under Shariya, father  is entitled to sole guardianship of child after he/she crosses seven years of age. As she is 13, you can obtain her guardian but only after Khula or Talaq.  

Obtain Khula than apply for guardianship. It will take about one year. 

Hello, 

1. You can certainly apply for guardianship if you can prove that thewelfareof the child is better in your custody and guardianship even if there's no qulanama.
2. That when there's no divorce and the custody has to be gained thrift a court order, it can take long as your wife can cause intentional delays. 
3. A better option in your case is to file for declaration of the qulanama as a valid divorce whereby the court will grant a declaration making your divorce internationally acceptable and valid. Besides you can incorporate your wife's consent in giving permanent custody of the child to you. 

You need to take a decree of divorce on the basis of qualanam from court in India under sharia act

Getting legal guardianship of a minor child can be a lengthy process. Depending on the state, it can take anywhere from a few weeks to several months. In order to apply for legal guardianship, you must have a Qulanama. This document establishes your legal rights as the child's father and is necessary for court proceedings. Without this document, you will not be able to proceed with the application process. Once you have the necessary documents, you can then proceed with applying for legal guardianship.

Dear client,  

As a Muslim father, you can apply for legal guardianship of your minor daughter without the need for a Qulanama certificate or Indian divorce. The guardianship can be obtained through a legal process in the court.

The time it takes to obtain legal guardianship may vary depending on the specific circumstances of your case and the workload of the court. On average, it can take several months to a year for the court to grant legal guardianship.

To apply for legal guardianship, you will need to file a petition in the appropriate court and provide evidence that you are a fit and proper guardian for your daughter. This evidence may include your financial stability, living arrangements, and ability to provide for your daughter's education and welfare.

In addition, you should also be prepared to address any concerns or objections that your wife may raise in the court. It is important to remember that the court's primary concern is the best interests of the child, and any decisions made will be based on this principle.

Rather than mutual consent divorce, both spouses may end their marriage through a Mubarat divorce, which is an Islamic form of divorce similar to mutual consent divorce.

Mubarat divorce is an Islamic practice that allows a couple to mutually agree to end their marriage without involving a court or a legal process.

You can better enter into a MOU with her in order to enable both the divorce and the child custody case getting disposed simultaneously 

You can give your consent for divorce while she consents for permanent child custody with you with no visitation rights to her and also to give NOC for taking the child abroad. 

This MOU contents may be pleaded as prayer in her divorce petition,   in that case you don't have to file a separate petition for child custody. 

You have to enclose consent terms in Mutual consent divorce petition 

2) consent terms should mention that you will be having sole custody of your child . That you would be at liberty to take child abroad 

3) no need to file separate guardian ship petition 

4) MCD takes 6 months . Guardianship petition may take longer 

- If she is agrees for mutual divorce , then she can file a declaration suit before the family court for getting divorce legally .

- Joint petition of mutual consent divorce is not applied in Muslim case.

- Further, you both can turn the said case in mutual divorce , and it can be granted within a short period of time 6 to 8 months. 

-  Further, you can also file the custody petition before the court same time for getting custody of the daughter permanently , and you can also mention the same in your divorce petition as well. 

Both the cases will be decided as per its own merits 

Dear client,  

The time it takes to obtain a mutual consent divorce or guardianship of a minor child can vary depending on the specific circumstances of your case and the workload of the court. However, generally speaking, mutual consent divorce is likely to be faster than guardianship proceedings.

In mutual consent divorce, both parties agree to the terms of the divorce, which can expedite the process. However, the court may still require some time to review the agreement and ensure that it is in the best interest of both parties.

On the other hand, guardianship proceedings involve determining the best interest of the child and may require more time. The court may also require further investigations or assessments to determine the fitness of the parent seeking guardianship.

It is important to note that the timeline for both proceedings can also be affected by any disputes or challenges that may arise during the process.

If you are concerned about your wife intentionally delaying the guardianship proceedings, you may want to consider including a timeline or specific dates in your agreement. You may also want to seek the advice of a lawyer to ensure that your interests are protected and to guide you through the process.