将文件从一个http终结点流传输到另一个

I am trying to stream a file from one http endpoint to another, and avoid storing large files on disk. I thought I had working with this code, but it is creating empty files:

    // out, err := os.Create(key)
    resp, err := http.Get("http://source_url.com/_content/" + key)
    if err != nil {
        log.Fatal(err)
    }
    defer resp.Body.Close()

    // now stream the file straight to the endpoint using put
    req, err := http.NewRequest("PUT", "http://dest_url.com/_content/"+key, resp.Body)
    if err != nil {
        log.Fatal(err)
    }
    req.Header.Set("Content-Type", "application/octet-stream")

    client := &http.Client{}
    res, err := client.Do(req)
    if err != nil {
        log.Fatal(err)
    }
    fmt.Println(key, res.ContentLength, res.Status)