I gave my dragon to my first character. I had started in Freeport on a different server to play with some old guld friends. After a few weeks I decided I just wasn't happy in Freeport or on that server. I started a second character on the server that my niece and her guildies played on. When they came out with the option to do character transfers in EQII I took it. It did cost me $50 though.
After the transfer I did the betrayal quest and moved her to Qeynos. When she finally got access to Qeynos I gave her full access to my second character's apartment. She put her pictures & Luclan statue (also DVD rewards) in the apartment. I also placed the baby dragon in the apartment. Now when my second character goes into her apartment she has full access to the art work and the dragon. She can pick them up, move, them or put them in inventory.