I wouldn't recommend moving to a country without any intention of learning the official language. Not only will you be at a disadvantage job wise (you'll be competing with all the other web developers who speak both Dutch and English), but it will also be more difficult to integrate and interact with people, even if there is a high proportion of English speakers in Amsterdam.
By all means do hunt for jobs in Amsterdam, but also make an effort to learn the language, even if you get a job where you aren't required to speak Dutch.
Now, I don't know what the web developer job situation looks like in the Netherlands, but unless there's a lack of web developers, my guess is that you will struggle to find a job. Not only because of the language, but because many employers don't want to go through the foreign worker work permit hassle if they can simply hire someone local.