In Virginia and Massachusetts a Principal must have the appropriate capacity to execute a legal document, such as a Health Care Power of Attorney. Although this standard varies from state to state, I generally use the "contract" standard/test; being, does the Principal have the legal capacity to execute an enforceable contract. If the answer is no, then the Principal most likely does not have the necessary legal capacity to execute a Health Care Power of Attorney.
Switching gears, it seems odd that you received advice against opening a guardianship in this case. There are various types and levels of guardianships generally available. If you are appointed the "guardian of the estate" then you are a Conservator. This brings with it a great deal of annual financial reporting to the Court. Alternatively, if you are appointed the "guardian of the person" you are not generally charged with the financial management of the Principal (and therefore less invasive annual court reporting); but instead, you are charged with the custodial (and therefore medical) decisions and care of the Principal.
I suggest you acquire qualified legal counsel in your state to assist you in this matter. Visit the attorney directory listing on www.WealthCounsel.com to find local attorneys near you who may be able to help.
An Illinois statutory form power of attorney simply gives you the right to do certain things in place of the grantor of the power and the grantor has to have the legal capacity to grant the power, it does not diminish the person who is granting the power to do things for him or herself. The power is usually used when the grantor is simply not available to be present when needed to sign something or transaction something. Moreover the Illinois form power of attorney does not grant the power to execute heath care powers or advance directives, it is strictly limited to financial matters. Worse yet, a power of attorney doesn't diminish the fact that the rights conferred belong to the grantor -- hence let's say you open a savings account in your daughter's name and endow it with a sum of money. It is your daughter's money and she could just as easily transact it as you could; that is no protection. And a durable power or advance directive does require legal capacity or, if that is not existing, legal surrogacy. In extremis as her next of kin you would most likely be called upon to make decisions for her if she is not decisional. But what I believe you want is a guardianship so that you can execute such documents, and if she does something contrary to your good judgment you can have it undone (which under a statutory form power of attorney is not the case - the grantor can revoke the power at any time and act on his or her own behalf). Moreover you may wish to establish a trust for her so that there is a trustee who "owns" her financial wherewithall, to help her with her financial needs and keep control over the money to prevent her from being defrauded out of it. Finally, you're coming to a free website for your daughter's future and both physical and potentially financial well being? Please hire an attorney who will help you set up the appropriate protections for her!
Clarify with the person who gave you the advice. As an attorney, if I am not clearly able to assess the capacity of the grantor, I would usually want to make sure my own assessment is supported with medical records available from a recent consultation with notations about capacity. In this case, however, I have serious doubts that a grantor reading and writing at a second grade level could be deemed to understand the nature of granting a power of attorney. Knowing only the facts stated in your question, I disagree with the use of a power of attorney and suggest that a guardianship is warranted. I would be pleased to work with you in this matter.