Mine tends to go to sleep about 1 and sleep for an hour or so. Sometimes he sleeps later/earlier or longer but we always wake him by 3 because we found it affected his bedtime otherwise. He's not keen on being woken up (neither am I!!) but he doesn't stay grumpy.
How's it going? I used to wake DS1 and take him straight downstairs where his favourite tv programme was primed and ready, and without comment hand him a biscuit and a drink of water. He would watch and consume, and be right as rain in under 10mins, ready to face the afternoon! DD used to like a drink of milk and mr tumble. Whatever works!
18mo DS sleeps 2 hours in the day - I have to get him up by 2:30 at the latest to go on school run, so sometimes its slightly less than 2 hours if haven't managed to get him in bed by 12:30. He then sleeps 7-7.
Could you try waking your DD after 60-90mins to see if that has an effect on her bedtime? Good luck!
My 18mo DD will not have a nap before 1pm at the earliest. She then wants to sleep for about 2 hours which will be at least 3pm when she wakes up. I then struggle to get her to sleep before 9pm. She wakes up at about 7.15am no matter what time she goes to bed. I'm worried she doesn't get enough sleep as she wakes constantly during the night. (a whole other thread)