You mention Advanced rest Client. Is that the same as REST Client? The one at restclient.net?
If so, then I found that using this to start the REST Client shows the windows connected to the tabs such as Response Header to be recognized as .WebElement.
If I start the brower from QTP and then navigate, it shows the objects as WinObjects.
SystemUtil.Run "firefox.exe","","C:\Program Files\Mozilla Firefox\",""
' Navigate to restclient.
I'm using QTP 11.
I can get the list of Add Ons I'm using if you need the list to compare.
Please let us know if this works.