at less than 6, your daughter is still quite young to really sit and study. i understand your concern, but trust me, i have two kids, 9 and 3, and i have been through this myself.
does your daughter get enough sleep at night? sometimes, the main reason for kids being grumpy and crying in the morning is because they need more sleep. i suggest you try to put her to sleep a little earlier than usual. my kids have to leave by 7, so i make sure they are asleep latest by 8pm, sometimes even earlier. it helps to keep them fresh in the morning when they wake up at 6. also, play with her a little while making her brush or giving her a bath. make those school-going activities enjoyable and fun, instead of a chore that she has to do.
as for studies, let her take her time. if you are worried that she is not able to cope up, help her learn through play methods. if she gets upset and hyper, let her take a break once in a while and just pamper her and be with her. this is just a phase, so don't worry at all :)
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Queen bee of 2 cheerful daughter