Would I be able to use Air Play, Apple TV, and an iPad running iOS7 in order to mirror an iPad running the Safari web browser onto an HDTV?

Yes.

Basic AirPlay: Assuming both devices are on the same network and that AirPlay is not turned off on the Apple TV, then simply tap on the screen when you are watching content you wish to stream to your Apple TV, then tap the airplay icon that appears in the control bar, choose the Apple TV from the menu that appears.

Mirroring: When displaying the content you wish to mirror on the iPad 2 (or better), iPad Mini, iPhone 4S (or better), swipe from the bottom of the screen, tap the AirPlay icon and choose your Apple TV from the list of devices (iOS 7 or better) or double tap the home button (quickly) and swipe the bottom row of apps to the right to reveal the playback controls, tap the AirPlay icon and select your Apple TV from the list of available devices (pre-iOS7)