Which one is right, J2 or H4?

My J1 waiver application was approved by the Department of State this March. I am now applying for H1B since my J1 will expire in November. My daughter's J2 visa was issued in Feburary and will expire by the end of August. My concerns are: 1) Is she still eligible to enter the USA with the J2 visa? 2) Does she have to apply for H4 to be here? 3) If she enters with J2, can she have her J2 transferred to H4 after my H1B is approved?

Thank you for your help!