If it is truly an uncontested divorce and you and your spouse agree upon all property/debt and support issues the court will accept your agreement and issue a judgement of dissolution of marriage accordingly. Please remember however that the court always reserves jurisdiction to act in the best interests of children such that child custody, support and related issues can be modified at a later date.
The Judge will almost always approve your agreement. In some cases of long term marriages where the division seems to be inequitable, some judges may require you to be in court in person and on the record as to waiving your rights and approving the agreement. In your case that shouldn't be a problem.
A weekly guide with tips and legal advice for each stage of the process.