Hi and welcome,
Yes, your partner should be tested before proceeding. Chances are he is not a carrier, but you need to know for sure. If he is a carrier, there is a 25% chance of having a thal major. I do not trust the odds at all, as I have known families with three thal majors, so I always say don't rely on odds to protect you. Hopefully, this won't even be an issue for you.
For yourself, you should be taking folic acid before trying to conceive, as this is recommended for all women trying to get pregnant and throughout pregnancy, as this has been found to reduce birth defects in general. Also, because there is a tendency for thal minors to have miscarriages, I always suggest natural vitamin E for its mild blood thinning properties.
In the meantime, don't worry. If your partner has never had anemia or shown any sign of thal, he is probably not a carrier. He should be tested to confirm this, but the chances are he is not a carrier. Your main focus now should be on addressing any health issues you might have and getting your body ready to try to become pregnant. Good nutrition is a must with thal minors, as is whatever exercise you can manage, so you are already on the right track.