I'm in a tricky part of my 3 year old's sleeping age, if she has a nap during the day at daycare it causes her to go to sleep at 10-11pm at night, however we have to be up at 0530am to go back to daycare at 6am. I'd like to know the recommendations of child’s age, developmental stages and needs around sleeping please.

Sleep time at childcare is a very common question from parents & child care educators & can be a difficult time for all.
What happens with her daytime nap when not in daycare?
Can the nap time at daycare be negotiated ie having it earlier in the day?

Red Nose does not have specific information about stages of sleep & child development.
You may find the information from Raising Children Network helpful
https://raisingchildren.net.au/toddlers/sleep
https://raisingchildren.net.au/preschoolers/sleep