I have done a portfolio, but really it's just my website

I don't apply for jobs with my local puppetry companies though, and don't expect to have a need for one, it may be different if you're intending on getting work with other people. I did do a stall at a market once and took a 'catalogue' with me... you'd be surprised how few people were interested in that as compared to watching someone work the puppets or pick them up themselves. I guess it depends on who you're approaching and what the portfolio is intended to showcase. (Ie. showing how you go about designing a puppet would work for a portfolio, with drawings and sketches; but for finished products people might prefer visiting your studio instead)
Speaking as one of the few people here who hates performing... There are jobs specifically for puppet builders/designers, and you'd probably get more work freelancing (ie. selling puppets at markets, online, commissioned for shows, etc) than just hoping to sign up for a company and leave it at that. However, and this is experience mainly within an Australian perspective, I've found that performers who build (or builders who perform) have more opportunities available to them. Which makes sense because you've got twice as many ways to apply for jobs.
If you're not familiar with it, I recommend heading to
http://www.puppeteers.org and looking at their bulletin board. The Puppeteers of America bulletin board is a great starting point for figuring out what kind of jobs are available and you can easily and informally survey it to calculate the no. of design/building jobs vs the no. of performing or combined jobs.