My two brothers were on this show in 1954 and I want to get a copy of the show. Does anyone know how to go about this or even find out who to contact?

Maybe try contracting the TV station that it original aired on. It was original shown on the KENI station which is now KTUU. Here is an article that talks a little bit about the show.
Hi There, Boys and Girls!: America's ... - Google Book Search (http://books.google.ca/books?id=hHZ3wYy7e9gC&pg=PA36&lpg=PA36&dq=Mother+Moose+Show+Anchorage+Alaska+1954&source=bl&ots=HfaCKWDmwz&sig=l81eC9oscSUics5YQR4Z1H5f4Cc&hl=en&ei=EAXTSbDwD9mDnAfQqsDiDw&sa=X&oi=book_result&resnum=1&ct=result)
I hope this helps some