Yes, H1 dependent can't work

If you both want to work, then you need to apply for H1 for each of you. For postdoc, NIW (EB2) is the fastest way and best way to apply for green card. EB1 is also an option if you have outstanding achievements. You and your wife can apply for NIW separately(two applications), then file the I-485s based on the first one approved. For NIW, you need to present yourself very well to increase the chance of approval, you may need a lawyer to do this for you.