I'd like to have a fence all around our property, so the dog we want to have can run freely.
この場合、次のような言い方ができますよ。
ーI'd like to have a fence all around our property, so the dog we want to have can run freely.
「飼いたい犬が自由に走れるよう、うちの敷地の周りにフェンスを張り巡らしたい」
to have a fence all around ... で「…にフェンスを張り巡らす」
ご参考まで!