Experts and BHG readers answer.
When to move & replant a palm tree
I assume that you're referring to Phoenix roebelinii, the pygmy date palm. If you live in South Florida, Hawaii, or other locations with little likelihood of freezing (or near-freezing) weather, you can transplant the tree any time of year. In areas with cold winter weather, avoid transplanting the palm until warm spring weather arrives. Also, avoid transplanting during extended dry periods, unless you pay close attention to watering the new plant.