Notice that Gandalf did not even speak at this point of the Council; he realized that it was what Eru had planned. In my opinion, that is the main reason he 'trusted' the Ring to Frodo on the Quest. So yes, I think that Gandalf was wise in letting Frodo carry the Ring, since it was obviously the choice of a higher Power. More @Wikipedia
Hover over any link to get a description of the article. Please note that search keywords are sometimes hidden within the full article and don't appear in the description or title.