Ibbie's Teddy Bear is crafted with Tailoring in Mabinogi (other). This page lists everything needed to make it, checked against the game as it exists today. The interactive planner lives in the Tailoring Companion.
How to get the sewing pattern
The sewing pattern is rank 5 and survives 30 uses; every crafting attempt spends one use.
Ibbie's Oldest Friend Quest: Talk to Ibbie in Bangor with the Skills keyword once Rest reaches Rank 2.. Requires Rest skill trained to Rank 2 before Ibbie offers the quest.
Materials
Expect about 1 attempt per finished item (99.9% average progress per attempt). Per-attempt materials are consumed on every attempt; finishing materials once per item.
Each attempt uses
2× Finest Fabric — weaving on a loom, higher rank
5× Tough Thread — weaving Thin Thread Balls
1× Old Teddy Bear Fabric — Obtained from Huw at the Puppet Workshop during the Ibbie's Oldest Friend quest.
Finishing (once per item)
2× Finest Finishing Thread — Buy directly from any general goods NPC shop.