Is it customary to include a dedication in an honours thesis?
Dedication generally comes in your front matter section in your thesis. It will depend on your university rules and guidelines. Generally "dedication" is not mandatory in most of universities. However it is advisable to check with your academic office. 

Quoting from Harvard guidelines for thesis writing,


  Front matter may include: acknowledgments of help or encouragement from individuals or institutions; a dedication; a list of illustrations or  of tables; a glossary of terms; one or more epigraphs—pertinent quotations at the beginning of a dissertation or a chapter


My personal opinion is that dedication gives emotional touch. It is good to have dedication page in your work.