Can I travel inside the US if I have my deffered action permit?

As you have already been approved under the DACA program, your departure is deferred for two years and you are allowed to work during that same period of time. If you are encountered by Immigration, you could show your deferred action grant along with the EAD and you would not be arrested unless there was another ground for which you are excludable. Due to the limitations of the lawyers.com forums, Alan Lee, Esq.’s (the firm) participation in responding to questions posted herein does not constitute legal advice, nor legal representation of the person or entity posting the question. No attorney/client relationship is or shall be construed to be created hereby. The information provided herein by the firm is general and requires that the poster obtain specific legal advice from an attorney. The poster shall not rely upon the information provided herein as legal advice, nor as the basis for making any decisions of legal consequence.

You are free to travel throughout the US.