Your sentence is correct. My daily morning routine: On weekdays, I usually wake up at 8am. I get out of bed and give my cat her breakfast first, then I start to get ready for work. Once I have picked out my clothes, I get dressed and brush my teeth. I say goodbye to my cat for the day, and then I go to work. I have tea at the office before I start working. On weekends, I sleep until 9:30 or 10, and then give my cat her breakfast. Then I cook breakfast, and eat while having tea. Then I brush my teeth and get dressed. I like to go for a walk in the morning on weekends.

If you wanted a more casual sentence, you could say - What’s your typical morning like?

You can just say "Could you tell me about your morning routine" without "daily". "Routine" already means something you do regularly, so "daily" is redundant. Anyway, my routine goes like this at least Monday to Friday: I wake up at seven, and listen to the news on the radio while I brush my teeth. Then I have a shower and get dressed. I make myself a breakfast of an omelette and a cappuccino. Then I wash the dishes and go to work.