This is Midsummer Cottage Retreat, near West Compton. It's a converted barn from the 16th century, so the beams are low in places and the walls are thick. You get the garden to yourselves, and it's a good size.
It's a one bedroom place, so it sleeps two, but there's a sofa bed in the living room for a third if needed. It has a 4 Star rating. That means it's been done to a high standard. Everything is new and works properly. The shower is good.
You can bring a dog. The garden is enclosed and there's a lot of land around for walks. There's parking right there.
It's a quiet spot. You're about half an hour's drive from Glastonbury Tor and the town. Wells is even closer, maybe 20 minutes. The cathedral there is worth seeing. The Glastonbury Tor page on English Heritage has the history if you're interested. Wookey Hole Caves are about 15 minutes away by car.
Inside, you've got a washing machine, a TV, and the wifi works. All the bedding and towels are here. The kitchen has what you need. There's a local pub within walking distance.
Useful links for the area: National Trust Somerset and Visit Wells.