F1 to H4 COS, I- 797C in hand

I am currently on F1 OPT which expires in mid-July and my husband’s H1B is approved for the year which will start in October 2020. His employer has filed for my H4 and I have received I-797C.
Considering my I-94 will expire in a month and new H4 will not start before October 2020,

  1. Do I need to apply for another dependent visa(COS) to bridge the gap or I am okay with the receipt in my hand?
  2. If I apply for another COS then what should be the start and end date for the same.

You will need a valid status to stay in US after your F1 i94 expires.

What is your husband’s status at this time? You will have to file a dependent visa COS if your husband holds a primary visa.

The start date should be after your current i94 expires. The end date cannot be guessed. You have to use your own judgement.

Related case:

My husband is currently on F1 visa but has received his I 797A for his H1. Do I still need to file for another COS or I am good with the H4 I 797C (for H4 application in process) in hand?

What visa type does your husband plan to stay on to cover the gap between his F1 end and H1B start date?

Your should read this cap gap explanation first.

He is on a valid F1 visa. He is not on Cap gap as his F1 OPT Stem is valid till 2021. His H1B approval has been received and his new I94 starts from 1st October 2020. So, he need not worry about going out of status.

You should have F2 then if you do not have any H1B pending for your case to cover the gap.