To begin with, I wouldn't do it alone for a few reasons. The first of which is experience, the second is that many new buyers think with their hearts instead of their heads.
I would take a knowledgeable person with me who can look at the pony objectively and look for signs that you may miss. I would make more then one trip and the first one would be without your daughter - you don't want the distraction or the "I'm in love with him" thing. Keep in mind that your daughter's life or at least her well being will be on this pony, so look carefully and don't be taken in by "I have someone else coming this afternoon ...". If you have to make a fast decision, walk away. It's better to take your time then be rushed into making a mistake.