perl -E'say "OK" if "123dog"=~/\A\d+[a-z]+\z/'
works for me. You're not using some stoneage Perl that didn't have \A, are you? Should have been there since before 5.8.
The one-liner worked for me as well and so I went back to my code (which I should have posted) and realized I forgot to chomp the input strings (the user was prompted to enter input strings and a regex). I chomped the regex, not the input strings. A novice mistake, I apologize!
In case you are using Eclipse withe epic plugin as IDE for development you can check your regular expression with the RegExp View. Also, in case you got leading whitespaces or a linebrake at the end of your string - you can easily see in debug mode in the variables view. For me always a great help.