A quick search on Ancestry site for 1850 census in Morris shows a John White, 50, with Ellen 42, Sarah 13 and Catharine 10 (all b. Ire), John 7, Mary 5 (both b. NJ). A Julia 20 b. Ire lives 2 doors away and there is another John White, age 19, living as a laboror on a farm in Chatham. this doesn't look like your family. There are a LOT of John Whites throughout NJ, notably nearby in Passaic and Sussex Counties - the subscription to Ancestry is worth it for the census images alone.