Yes, you will need two DS's to trade between HeartGold and Platinum. You have the option of using the Union Room for trades/battle where you can complete with wireless link up, or you can use the Wi-Fi room and do trades/battles with others who have Wi-Fi around the world.
Other than this, there is the Pal Park, but that is only for use of migration with R/S/E/FR/LG using the GBA Slot on a DS/DS Lite.