"There is one dog at his house."
They keep tricking me on this one, the counters supplied in the word bank are hiki and biki, but we need picki for a counter of one. Therefore only 匹 is accepted since ぴ is not supplied. (Obviously just for those of us who are using the word bank and not a Japanese keyboard)
Addendum: は can also be used idiomatically to mean "at least". With that in mind I suppose your sentence could be taken to mean "There's one dog at his house, at least". Not sure how natural it sounds though. は is often translated "as for..."; the sentence would end up meaning something like "As for one dog, there's that at his house [as opposed to five dogs]".
It's because Japanese doesn't have articles (a, an, the). If you said 犬がいます it would be ambiguous. It could mean "There is a dog" or "There are dogs". If you want to specify it's one you have to say 一匹 but then the English translation sounds a bit weird when you do it as "one dog" to make the point that we're learning about counters/classifiers. It's a pedagogical translation, not a literary one.
Having the word "at" in the English sentence leads me to believe they want the particle で, but 彼の家で一匹の犬がいます。 is not an accepted answer. I don't think には is incorrect here, but I think で should also be accepted.