No animal can meditate. The main difference between human beings and animals lies in their capacity to achieve the meditation state.
Animals can experience only three states of consciousness — waking, dreaming, and deep sleep, which does NOT include meditation, the level beyond the mind’s three states of consciousness. But a human being has a capability to experience all four states of consciousness — waking, dreaming, deep sleep, and meditation (turiya in Sanskrit).
You may like to refer to the book, Building a Noble World (ISBN: 978-0974919706) for a thorough explanation of the meditation practice in Chapter 3.