Can a H4 minor travel with F1 parent, without the H1 parent accompanying them?

I will be starting my MS this fall. Once I get my F1 visa, I will be travelling to US with my minor daughter who is on H4. Since my husband (primary H1 holder) is already in US, he will not be travelling with us. My question is, will my daughter face any problems at the port of entry because she is travelling with a parent on F1 and not the primary H1 holder?

Should be fine. You should carry copy of H-1 holder’s 797 approval notice, letter from employer confirming the employment and contact details.