Linda June Lewbel, performing under the stage name Bunny Lewbel, was a child actor. She appeared in two films, "Road to Bali" (1952) as 7-year-old Lala; and in "I'll See You in My Dreams" (1951) as 6-year-old Irene. More info about these movies can be found at http://us.imdb.com/Name?Lewbel,+Bunny

She also played Danny Thomas' daughter on TV in the 1950's. Danny Thomas was a host (along with others on a rotating basis) of the related variety shows "Four star Revue," "All Star Revue," and "The Colgate Comedy Hour." Out of these grew "Make Room for Daddy," which was also known as "The Danny Thomas Show." Cast lists I've found for "Make Room for Daddy" do not list her (see, e.g., http://timvp.com/dannyt.html), so she was likely in the earlier variety shows. In particular, the web site http://www.geocities.com/chrisvil40/efilmog3.htm has the following:

All Star Revue NBC 11/17?/1951 Comedy Variety Host: Danny Thomas Other guest stars: Kay Starr, Joan Holloway, Bunny Lewbel

She also appeared as a guest star in “The Runaway Heart,” October 2,1951. This was episode #65 of “The Armstrong Circle Theatre,” a dramatic anthology series that ran on NBC throughout the 1950’s. see http://www.tvtome.com/tvtome/servlet/GuidePageServlet/showid-4522/epid-357291