Nope. It's not too early. My rule of thumb is that I don't wrap until the tree is in the stand with lights on. Because then I want to put the gifts under it. It keeps me honest about getting the tree decorated.
But once the tree is up, if I have gifts that aren't going to be kept hidden until Xmas Eve, then they go right under. OR unless it is some sort of weird box that they will know just by seeing the box what is in it. :(
For those things, they usually are kept at a friend's until closer to Xmas. When I can bring them in and tuck/hide them behind other gifts under the tree. My kids don't move stuff around once it is under the tree... no shaking, etc. They just don't. I don't really know why... I guess they just sort of consider it all off limits. Which is fine by me. :)
What I would likely do, if I were you, is I would put 2 or 3 things out now. Then in a day or so, put another couple of items out. Then after another few days, add some more... then you will have room in your current "hiding spots" to keep the rest of your shopping until you get it wrapped as well. I have been known to hide gifts in my china cabinet---my kids would NEVER think to look there!!