No, it's not a good career move. But the fact that it's not a good career move has not much to do with the language.
Positioning yourself as a "X language programmer" is IMO not a good career move, although for a very few languages (C, Pascal (70s/early 80s), C++ (80s), Java (late 90s), perhaps .NET (00s)), and a timeframe much smaller than the average length of a career (a few years vs 35 to 40 years) its doable. Although you position yourself as not flexible.
Gazillions of Perl programs are written by people who aren't on the payrole as a "Perl programmer". Instead, they have a much broader function (and hopefully that reflects in the amount of money they can bring to the pub), and they wield Perl as one of their tools. Perhaps their most important tool.
To make an analogy, do you think it's a good career move to position yourself as a "hammer wielder"? Or do you think that it's better to become a "carpenter"?
You can't move from Perl to .NET, VB, or really even C
I'd say that C is the closest relative of Perl, and that the more you know Perl, the easier it is to code in C. And some things are easier in C than in Perl.