H1B to H4 transfer due to maternity reasons

[chingi24]

I came to USA in 2001 on F-1 (got my SSN then) and got hired by a reputed company who processed my H1B starting October 2006. I am on H1B since then. Now due to my health reasons (pregnancy complications) my doctor has advised me to quit working for a while. I now want to change my status to H4 (my husband has H1B through his employer). Can anyone tell me what all do I need to do apart from filing I-539 ? Will I be considered out of status the day I quit ? Also, will my SSN be invalid while I am on H4 ?
I will appreciate all the help from members on the same.
Thank you