What you need to ask yourself is...what is information? How do you know when "more" or "less" information is present? This can get pretty technical, but for now let's keep it intuitive, and see where that gets us.
I don't think any creationist denies that a gene can be duplicated. Nor do I think any creationist denies that one of these genes can undergo a mutation. Now you have two genes, one different from the other.
By any reasonable definition I know for the word "information", the example I presented is an example of increased information through natural mechanisms.