What does it cost to make my daughter guardian of her 12 year old daughter for the purpose of inheritance money?

I assume the person with the $150,000 has already died.   If not, it would be better to change the estate plan to set up a trust for your granddaughter.   Your daughter would need to file for a guardianship of the property, with total cost of about $2500.   The child's father would have an equal right to be guardian, which could, depending upon the situation, be an issue.  

It is unlikely that any court will allow this.  Regardless of what money is held in trust or in a court registry for the benefit of a minor, parents have a duty of support.  It is too easy for a parent to accidentally dip into the wrong account.