Create an Proxy server - Forward all headers, body, everything, but change the URL

Question

• We have a private server that I cannot access.

• We have another public server that I can access.

• The public server can access the private server. (ie. A proxy server)

So I want to build an ASP.Net framework app on the public server that will simply forward all query parameters, body, headers, everything, to the private server.

When I make a route, how can I just forward everything to the private server's URL?

I have this so far but not sure if I'm thinking about this the right way. I feel like there's a way that is more automated:

[System.Web.Mvc.Route("search")]
public object Search()
{
    var request = HttpContext.Current.Request;
    var BaseUrl = "http://my-private-server-url";
    var client = new RestClient(BaseUrl);
    var newRequest = new RestRequest(request.HttpMethod);

    // The code below errors:
    // Cannot convert from
    // 'System.Collections.Specialized.NameValueCollection' to
    // 'System.Collections.Generic.ICollection<System.Collections.Generic.KeyValuePair<string, string>>'
    newRequest.AddHeaders(request.Headers);

    // How do I forward the request body too?

    var response = client.Execute(newRequest);
    return response.Content;
}