Is it possible to define an automorphism on the structure $\mathfrak{Q}=(\mathbb{Q},<)$ and what would be an example?

Question

In this case < is interpreted as the normal comparison operator on $\mathbb{Q}$. My current thoughts say no, since there is no possibility to define a function with just the < operator and we are quite limited by the signature. My overall goal is to prove that there is no function $\phi(\mathfrak{Q}) = \lbrace 0 \rbrace$ and I think that an automorphism is the way to go. But somehow I cannot come up with an automorphism on $\mathbb{Q}$ with the given signature.