To start with I'll answer your question directly. Yes contract roles are a viable way to gain industry experience and enable transitions into permanent roles. While I certainly can't make this decision for you (I don't know the Dallas market) I'd be happy to braindump what I normally look for as a QA hiring manager for web companies in NC.
Because I work in smaller startup environments these candidates are expected to be able to grow into a cross functional QA role (usually manual testing + some form of automation). Many larger companies may have different expectations. During an interview, I expect junior-level to be able to demonstrate a testing mindset in addition to speaking to several of these areas of development knowledge...
- Basic programming, at least through OOP
- Background with selenium or other application/web driver tools
- Familiarity with HTTP requests (verbs, some understanding of how to use the common ones, background in http gui clients like Postman)
- Depth of experience using SQL (CRUD then into joins at minimum)
- Use of something like dev tools in Chrome or Firebug in Firefox during their testing.
- Ability to use linux command line to navigate a file system and do other basics
If a candidate can actually respond confidently to many of these areas I usually know I've found someone primed for growth into more advanced QA roles.
Now back to you specifically, from your original question you mention
- Experience in 2 programming languages suitable for writing automated tests
- Some understanding of the technology used to construct websites
- An interest in the testing area of software dev specifically
While I'm working off of a really short resume/CV my initial impression is that you could probably make more than 45k in a number of job markets (including mine) if you're able to interview well and back up those skills. This might be a viable entry point into the industry for you but I'd encourage you to not settle and use sites like Glassdoor to gauge salary ranges for your region as your contract nears an end. The market for competent, technical QA is white hot right now and we shouldn't sell ourselves short.