If you are eligible for H4 EAD (not all dependents of H1-B are) you will need to apply for both the H4 and EAD.
As to whether these can be done concurrently such that you get H4 and EAD simultaneously, that will be a question for an H1 forum, not here.
If it cannot be done simultaneously, you will need to decide if you can afford a period without work authorization, as the instant you get H4 without EAD you can no longer legally work in US (until the EAD is issued)