Please let us know my daughter is in L2 visa extension. Can we apply F1 and H4 visa in USCIS one month after other at the same time?
Only if primary is H1B, you can apply for H4 for your child under 21 age. If you are L1, then your daughter qualifies for L2 until she is under 21 age or if she is going to ageout soon, you can apply for COS from L2 to F1.
Note that there is a long delay in processing of COS to F1 so you must plan couple of years in advance before the child turns 21.
If the COS application is pending and meanwhile the child turns 21, you will need to file a bridge application for COS to B2 to bridge the gap between when the child aged-out and the COS approval to F1, otherwise the child will be out of status and the COS to F1 will get denied. If this happens, the child will need to leave US and come back with F1 visa stamping.