The word "schlepped along" implies a sense of weariness, heaviness, or slow movement. Some antonyms for this phrase could include words like fly, soar, buoy, or glide, all of which convey a sense of lightness, ease, or effortless movement. Other antonyms might include words like sprint, dash, race, or bolt, which suggest a fast pace or energetic movement. Still other antonyms might include words like skip, dance, hop, or frolic, which convey a sense of joy, playfulness, and carefree movement. Whatever the context or tone, there are many antonyms to choose from when seeking to contrast the idea of "schlepping along" with a different type of movement or action.