In SharePoint 2010 you will find that you can add links with query string to Quick Links (aka Current Navigation) using the UI without any issue. If you enter something like http://mySite/pages/myPage.aspx?key=abc into the dialog, then it’d happily accept it.

If you tried doing this by code however, you may find that the link is saved, but the query string is removed. To achieve this with code, you will need to add a key to the link’s Properties bag after it has been created. Below is the code for doing this.

using (var site = new SPSite("http://mySite"))
{
    using (var web = site.OpenWeb())
    {
        var newNode = new SPNavigationNode("My Link", "pages/myPage.aspx");
        newNode = web.Navigation.QuickLaunch.AddAsFirst(newNode);
        newNode.Properties.Add("NodeType", "AuthoredLinkPlain");
        newNode.Properties.Add("UrlQueryString", "key=abc");
        newNode.Update();
    }
}

The magic key is UrlQueryString.

Note that when you add a link as the top level link by code, it will default to the Heading type. To add it as the Link type, you will need to add the NodeType key to the Properties bag. I have written about this here.

If you examine the Properties bag of an existing link added via the UI, you will find other interesting keys, such as the target for the link.