Ok, this requires a huge caveat. For this build to work you need the GM to agree that somehow your character acquired a Cape of the Mounteback or other item that lets you dimension door before you became 3rd level.
I don't think that would work. Unlike the Teleportation Mastery feat which specifically states that the spell you cast through the item is a spell-like ability, normal command-activated magic items do not work like that. The Dimensional feats require you to be able to cast Dimension Door as a spell or spell-like ability, but activating an item that duplicates the effect of Dimension Door does not count as having access to it as a spell or spell-like ability. It is pretty much equivalent to having a wand of Dimension Door.