Check local building and fire codes before you do any design/planning. Most areas require a specific distance between a wood burning appliance and any burnable flooring.

Build the pad and carpet up to it. You can secure the carpet with baseboards.

But like HandyMac said, check local coding, and the installation manual for the unit you're getting installed.

Tack strips, not baseboards. The carpet won’t pull away.

Build the pad and have a carpet man come in and install tackstrip and stretch the carpet into place. If the carpet is not stretched properly, it will cause wrinkles in the carpet down the road....then you'll have to have a carpet man come out and fix.. May as well do it right the first time.

Carpet without pad is often called "glue down". Where do you plan on putting the tack strip that will not cause a hump? I generally create a small recess around the edge of the pad to tuck the carpet under, just like baseboard. 1/2" should be plenty, or ⅜x⅜ if the carpet is only ⅜ thick, for example .