В документации Qt 4.6 в разделе устаревших классов есть QHttp, но не написано что использовать вместо него.
Все сказано:
This class provides a direct interface to HTTP that allows you to download and upload data with the HTTP protocol. However, for new applications, it is recommended to use QNetworkAccessManager and QNetworkReply, as those classes possess a simpler, yet more powerful API and a more modern protocol implementation.