pretty close. から~まで is like "from~until;" you had them switched. Also, since Kyushu is only in Japan (and written 九州/きゅうしゅう), it's not necessary to specify any further than that. Lastly, instead of 行く (go), I'd say 旅行する/りょこうする (travel). Both are alright, but the latter is more specific to a trip, as opposed to other reasons for going there.
来年の4月11日から17日まで家族と(一緒に)九州に旅行することにしました。