Quickbeam is also a name (in English) for the Rowan Tree, which was the tree that Quickbeam loved the most.
It should be noted that the English name "Quickbeam" comes from the Old English meaning of the word "quick", that is "alive". (The Rowan is also referred to as the Tree of Life). In the book, Quickbeam gets his name because he is quick to make speach (for an Ent) and just happens to have an affinity for the Rowan. Being the philogist that he was, Tolkien must have been well aware of the real meaning of the word quick, and was just using it in these two different contexts as a joke.
It would be interesting to find out if the word quick and alive derived from each other in Quenya, Noldor or Sindarin.