To move a unit from hq to a planet do you pay resources?

No. However remember that you can't actually deploy them normally, they all MUST go to the planet with the Warlord and they show up exhausted.

No. Units in the HQ move to planets with the Warlord when it is committed during the Command Phase. This is a separate game effect and you are not considered to be "deploying" the units, so you do not have to pay the cost to deploy the unit in order to move it.