Cast a Type to a class

If I have a class defined like this:

public class className
{
    public object this[string propertyName]
    {
        get { return this.GetType().GetProperty(propertyName).GetValue(this, null); }
        set { this.GetType().GetProperty(propertyName).SetValue(this, value, null); }
    }

    public string Foo{ get; set; }
    public string Bar { get; set; }

I can of course set and get the values like this:

className d = new className();
d["Foo"]="abcd" // set
string s = (string)f["Bar"];

(thanks to Eduardo Cuomo for his answer here)

But what I'd really like to do is something like:

Type target = Type.GetType(DocumentType);

// loop through list of key-value pairs and populate the data class defined in target object Type
foreach (Dictionary<string, string> PQList in LPQReq)
{

foreach (KeyValuePair<string, string> kvp in PQList)
{
    // populate the member in the data class with the value from the MQ String
    target[kvp.Key] = kvp.Value;                                                
    }    

but this wouldn't compile as Cannot apply indexing with [] to an expression of type 'System.Type'

so how could I do that?

I can use dynamic of course, but maybe there is a way to cast my Type to my target Class?