This is just me, but given your budget, if you're going the Canon route and buying new, I'd look at going down to the 60D (or possibly a used 50D), rather than the 7D, and throw the extra money towards glass. Birding lenses aren't cheap. Among birding photographers, the general advice is that a 400mm lens is going to be the minimum reach you're going to need, and you'll probably want more (or you'll end up adding a teleconverter). Most of the really fantastic birding shots you see are taken with superteles in the 500mm-800mm range. These are EXPENSIVE. A 400mm lens tends to be in the $1000-$2000 price range, and those are the cheapest superteles. When you start looking at 500mm and longer lenses (Sigma aside), or something faster than f/5.6, the prices will leap up into the $3000-$8000 range.
My recommendation would be to get a $1000 camera or below, and go for a 100-400L (EF 100-400mm f/4.5-5.6L IS USM, which is around $1600 new. Bodies come and go--they're updated like most other digital electronics every three to five years and they depreciate like crazy (when a 50D was new, it cost around $1200, three years later, you can get one used in the $700 price range). Your lenses are where the bullk of the money you spend is going to stay with you. Their resale values stay high. In three years, you may only lose $100 (or make a small profit, actually, with the price increases going the way they are) on a 100-400L.
On the Nikon side of the fence, a D90 would be similar to get a 50D on the Canon side of the fence, but lenswise, you're probably going to end up looking at Sigma choices (120-400 OS or the 150-500 OS or 50-500 OS), since Nikon's 80-400 VR is not an AF-S lens, and the complaints are generally about autofocus speed--something you really want if you're going to be shooting flitty little passerines, and Nikon's AF-S supertele choices are going to be well past the $1500 price point.
BTW, 400mm is not magic, and it
still won't be close enough. I have the $1100 EF 400mm f/5.6L USM prime lens (no stabilization, no zooming) for birds in flight, and I still crop all the time.
Now, you don't have to start with a four-figure 400mm lens. You can work your way up there gradually via a much smaller and more affordable (~$600) EF 70-300 IS USM (the black non-L version). But at a certain point, if you're really into bird photography, the need for the reach and an ultrasonic focus motor is going to consume you. At least, that's been my experience. I went from the el cheapo EF 75-300 III (non-USM, non-IS version) to my L prime, and I've never looked back.
Canon 50D. EF 400mm f/5.6L USM, iso 800, f/5.6, 1/640s. handheld.
White-Tailed Kite, juvenile.