If I have no cards in hand, do I still draw a card when moving with Traveling Merchant?

Yes, you still draw 1 card.

Traveling Merchant says "discard 1, then draw 1" — the discard and draw are separate instructions resolving independently. When you have no cards in hand, the discard instruction is simply ignored (you can't discard from an empty hand), and you proceed to draw 1 card as normal.

This follows the general rule that effects resolve as much as possible (Rule 422.4, Rule 055). The key distinction: if the ability said "discard 1 to draw 1" or "discard 1. If you do, draw 1", then you wouldn't draw without discarding — but Traveling Merchant's wording lets each part resolve on its own.