What visa you will be holding while studying for LLM, F-1 or H-4?
If you enter as an F-1, you may need to switch to H-4 if you want to apply for EAD.
However, since your spouse has his I-140 approved, it would appear that you have intention to immigrate to the U.S. when you apply for H-4 (either now or later). You H-4 visa application may be denied as such. Talk to an immigration attorney for your situation.
My bad. Both H-1B and H4 visa allow dual intent. Therefore, if you apply for H-4 visa now or later, immigration intent should not be held against you.
On the other hand, applying for F-1 visa seems to be problematic since that is a non-immigration visa. Most likely your attorney would recommend H-4 visa for you to enter the LLM program.