Fennel, like carrots and dill, has a long tap root and does well when direct sown. Take care not to damage the root. You will have plenty of time to sow these seed (indoors and out). I would start my seed in March or April to avoid spindly plants.
Yes, this will thrive in New Jersey. To assure your success, start seed a few every week for 3 or 4 weeks. Make sure the soil is warm - at least 50 degrees. Keep soil moist, not wet.