I remember the very similar backlash when Tennant was announced, likewise when Catherine Tate was announced as the new companion - and both went on to recieve tons of fan accolades. I think the new guy will do fine!
I found "The Ruby in the Smoke", a mystery movie where Matt Smith ironically plays the sidekick to Billie Piper's Victorian sleuth character. Skipped through a couple scene featuring the guy, and you know what? He does have a very Doctorish air about him, showing a maturity in his portrayal that goes beyond his character's obvious youth.
While Moffat obviously faced pressure to do a more stereotypical Doctor in casting, he went with what John Nathan Turner did when called upon to fill the role in the shadow of Tom Baker's excellent portrayal: he went with a younger guy. Peter Davison was already well known from "All Creatures Great and Small", but flew int he face of the idea of the older guy flitting about the universe. Moffat is on record as saying that the fifth Doctor was his favorite (and is one of mine too), so it comes as no real surprise to cast a way younger guy.
And obviously, the continued mega-success of the franchise is dependent on Matt Smith being able to take on the role AND have the fans of the new show love him. The BBC have doubtless analyzed and approved of Moffat's casting choice and the reasons behind it. We just don't know yet what the old school fans will think, now that lots of them have children or even grandchildren of Smith's age. Not that we really mattered THAT much compared to the legions of modern Whovians (especially the teen crowd who used to be the pre-teen crowd that loved Eccleston and were introducted to Tennant) who'll doubtless lock onto him.
Still though, we have three whole hours of David Tennant's Doctor to go before we even get a taste of what Smith will bring, with Moffat's deceidedly poplar writing and production backing him up. I've liked every Doctor for different reasons, and I expect to like this one as well. Bring him on, I say!