I've found 70-300 to be a pretty good range for wildlife. You'll have to back off a few feet from the dragonfly, but you'll still get great shots of it. If I were you, though, I'd spring for a stabilized lens. I switched from Nikon's 70-300 AF ED to the 70-300 AF-S ED VR lens, and saw the results immediately.
These are links to a Canon lens and a similar Sigma: (Tamron doesn't seem to make one with image stabilization)
http://www.bhphotovideo.com/c/product/397663-USA/Canon_0345B002_70_300mm_f_4_5_6_EF_IS.html
http://www.bhphotovideo.com/c/product/652369-USA/Sigma_572101_70_300mm_f_4_5_6_DG_OS.html
You do pay a lot more for these, though. If they are out of your range, the newest Canon EF 75-300mm f/4.0-5.6 USM is only $200 (you might as well go genuine Canon at this price). Make sure you get the USM version, though, because it's much quicker to focus (not to mention quieter!)
(I had a link for this one, but the forum flagged my post until I removed it. I'm sure you can find it on your own
)
Also keep in mind that these lenses don't go very wide. You can get an 18-whatever, but my guess is that the quality will suffer, unless you stop at 18-200, and give up the extra reach. I personally think you'd be better off taking Kiwi's advice and just adding a second lens. A 50mm 1.8 gives you a fast lens for pretty cheap. You can get an 18-55mm for around $150, or step up to a 17-85mm for around $450. It depends on what else you like to shoot.
Personally, I rarely take my 70-300mm off when I'm birding. I also have an 18-70mm that I use for travel snapshots or the odd landscape. When I'm birding, though, I've never really found a need to go wider than 70mm.