Traditionally, Dragonlance cosmology has been divided into six areas: the material world, the Gray, the Elemental Planes, the Dome of Creation, the Hidden Vale, and the Abyss. The 4th edition D&D cosmology is divided into five main areas: The mortal world, the Feywild, the Shadowfell, the Astral Sea, and the Elemental Chaos. Though there are similarities between these two models, they do not immediately seem to be particularly compatible. However, I will demonstrate that with only a tiny bit of reimagining, they are entirely interchangeable, and that virtually all published 4th edition D&D materials on the planes can be used in a Dragonlance game without trouble.
The Gray has been traditionally defined as a sort of mixture of the ethereal plane, the plane of shadow, and the astral plane. It’s the great sea of chaos, in which the material world is but an island. It is thus very similar to the 4th edition Astral Sea and Elemental Chaos. Furthermore, the new Elemental Chaos neatly encompasses the 3rd edition Elemental Planes. The Astral Sea and the Elemental Chaos are simply two contiguous “rivers” in the Gray, which encompasses both. They are not separated into ‘above’ and ‘below’ the material world, but are simply two channels twining about each other in the boundless ocean of chaos.
There is a long tradition in Dragonlance of so-called ‘pocket planes,’ smaller planes of existence created for a particular purpose by a particular agent. The 4th edition Feywild and Shadowfell fall very easily into this category. The Feywild is a large ‘natural’ pocket plane, full of fey and mighty beasts. It was created by the nature gods, in all of their contradictory vibrancy, placidity, and violence. The Shadowfell is a large, somber pocket plane associated with death. It is overseen by an austere aspect of Majere, a reserved aspect of Chemosh, and by Gilean himself.
The Dome of Creation, Hidden Vale, and the Abyss are the domains of the gods of Good, Neutrality, and Evil, respectively. They are located as ‘shores,’ surrounding the Gray, and touch both the Astral Sea and the Elemental Chaos. The Dome of Creation lies above the Gray. The True Abyss lies beneath, and is different from the 4th edition Abyss. The Hidden Vale lies between the two.
But how do you handle some of the more obscure or bizarre planes you come across? Some, like the Nine Hells, the 4th edition Abyss, and the 3rd edition Positive and Negative Energy planes, can be incorporated into your game as pocket planes in the Gray. Others, like Sigil, probably lie beyond the Gate of Souls, as they contain portals to other D&D worlds. That said, the convenient answer to all such questions is just ‘pocket plane.’ Placement is up to you.
A note on interplanar travel: such journeying in Dragonlance is traditionally quite difficult, especially to the domains of the gods. There are numerous portals into the Gray (and presumably into many of the larger pocket planes), but they are typically unknown to all but the greatest sages and guarded by Astral beings. While there’s no reason you can’t let your fourth-level party go to the Feywild, it’s not very "Dragonlance" for it to happen. That said, if they’re going to go to the Feywild to do something cool, I would be the first to encourage you to let them go there. Fun takes precedence over canon.
For further reading on the planes of Dragonlance, consult Holy Orders of the Stars, pages 77-78.