It certainly could keep happening in the future, it may have happened before also! The web is an open platform, and that has pros and cons. One of the cons is that it is very easy to publish whatever you want, such as copies of somebody elses site or content.
However, tricking Google is another matter. The site I used to work for has had probably hundreds of other sites steal content from it, some of them really egregiously (IE mirroring the entire site). It didn't matter though, because our site had a better reputation and had the content first. For example, let's compare your site to that other domain:
1) Your site was registered over 4 years ago. The knock-off site was registered 6 months ago.
2) Your site is hosted by a reputable web-host, linode. Their's isn't (or at least the whois for their IP range doesn't look reputable).
3) You had the content first.
4) Your site has some reputable incoming links, their doesn't.
5) Their site's IP is hosting tons of other sites, yours isn't (I'm assuming)
You are obviously the more reputable site, and that is why you are going to rank and they aren't.
The best defense is just to look more reputable than your competition --- the easiest way to do this is to be more reputable than them!
Three quicks things that I noticed you might want to improve:
1. Change the http://doremi-nj.com --> http://www.doremi-nj.com redirect from a 302 to a 301. A few incoming links are coming to the non-www version of your site, and theoretically a 301 is better for passing SEO juice than a 302. (In simple cases like this I'm sure Google figures it out anyways, but might as well help them).
2. Make sure you are giving Googlebot a sitemap with links to all your content to help them crawl it first. There isn't one in your robots.txt, so I'm not sure if you have one. You can just upload this directly into Google Webmaster Tools as well.
3. Have better meta descriptions. For example for the search "guitar lessons livingston nj", you come up 2nd. Very good! But, the snippet for your page is "Do-Re-Mi School of Music & the Arts93A South Livingston Avenue,Livingston, NJ973-758-1500 We offer instruction in Acoustic and Electric Guitar and Bass, ...". This is not a good snippet. For your main 20-30 landing pages (which you can find in GA) write custom meta descriptions that are going to look good in the Google snippet. This will not only directly help your traffic, but this is also is a good reputation indication! Human written meta descriptions look more human than robotic ones.