放牧されてて is the casual contracted passive progressive (放牧されていて). 牧羊犬 (ぼくようけん, 'sheepdog') is a specific compound. いるわ uses the feminine sentence-final わ. 一度訪ねてみてはどうかしら uses the suggestion pattern ~てみてはどう ('how about trying') with the feminine かしら ('I wonder'). The speaker is a woman enthusiastically recommending a pastoral outing.