Pete,
take his words with grain of salt...
first of all, although he probably said this mistakenly, the SEC would not give a crap, the IRS might. And even that, I doubt because you were not given this money to control for her. It is your money, do with it as you wish!
secondly, I purchased some stock for my godchild when she was born...bought the stock, got the cert, and it's hanging on her wall. You don't need to set up an UGMA or anything like that. If you want to keep it in an account, however, you may need to.
scot