Hi Luka,
I suggest, if possible try to come over here for a longer period, 3 months at least....and preferably on a DN visa.
As Vi has pointed out, the best way to get a job here is through personal connections and networking.....and, it takes lot of patience and time.
You may get some opportunities for freelancing and part-time works, but when it comes to finding someone to hire you on a full-time contract (with WP etc.) it is extremely unlikely and depends solely on luck. If you are lucky, you may get one. Otherwise, it can be bit frustrating.
As for getting hired from outside of VN or via VN Works etc., most of these happen for senior positions, least likely in your case.
Try to be fluent in German, that may open an odd opportunity for you somewhere.
Honestly, I was and still am on the same boat as you are. I came to VN for a month to try my luck, now on a short extension. In these one and half months, I got at least ten offers for part-time works, including teaching English, Soft-skills, CRM, ERP etc etc.. but what I really need is a full-time job (contract), so I can stay here and make plans for future with my fiancee.
For the time being it seems unlikely, I have to go back and explore other options like doing business, starting my own school etc. which I never thought of before. I am a "never say die" sort of guy anyway!!
The funny thing is, last month I got a full-time legit offer from a university in China at a reasonable pay....but none from VN yet!! You see how frustrating it can be sometimes in VN when you are looking for specific career opportunities. And, I am neither new in VN, nor less experienced or qualified in my domain in anyway. Still, the trend in the local job market is something very unpredictable and bit prejudiced as well at times. May be, the timing was wrong for me!!
My suggestion to you is, before you come over here, make a definite game-plan on how to invest maximum time in exploring every possible opportunity out here in VN.
Whenever possible, just walk in to talk to the HR with your updated Resume at hand.
Be flexible to accept and adapt to new roles (other than QA) as long as they are relevant to your qualification etc.
Be open to jobs from any part of VN, not only in HCMC.
Since you have a degree in Chemical Engineering, there might be some (although rare) opportunities here in VN.
Use careerjet.vn website to search for jobs. This is an aggregator site that shows up all relevant jobs from different job-sites.
BTW, a quick search with "Chemical Engineer" returned quite a few job-links there. Please check those out.
Good luck, mate!!