Welcome to the board Marciad
If you feel it's time to give her a deadline, then it's probably time. At age 21 she should at the very least be working if not in school full time.
What is her Learning Disability (LD), if you don't mind my asking? Could this be some of what is holding her back as far as stepping over the hump into adult responsibility? Objectively how ready do you think she is for the adult world? Where would she go? How would she eat? Will you be able to give her the deadline and follow through when she doesn't live up to her end?
I'm not trying to talk you out of telling her it's time to fly from the nest, just trying to help you to be realistic as you take this step.
My youngest, Nichole, was reluctant to leave home and step into the adult world. Although by 18, she had already transitioned into doing everything for herself such as doctor appointments, school registration, getting her drivers license ect. At 20 when she made the off handed comment she would just live with me forever.........It was my wake up call. Nichole was easy to live with. She did her own things, helped around the house, followed house rules, took care of her daughter, ect. But that "I can live with you forever" uhhh no. About a week later she was given until September to find her own place to live. (I gave her about 5-6 months notice) As I recall she moved out the beginning of sept of that year, she'd rented the apartment in aug but had to wait for it to be cleaned up.
When I first told her she was deeply hurt and thought she'd done something wrong. So I sat down and explained it to her. I told her she was already doing all the things an adult does, just not in her own house. The only things she had left to learn was about paying rent and utilities. That I realized that step could be scarey but I had all the faith in the world in her and she'd be much happier in her own place. So, scared to death but knowing when mom says something mom means it, she started apartment hunting.
I don't know what level your daughter is functioning at. But if you can get her cooperation.......you might want to sort of transition her into this deadline to move out thing by first having her handle her own affairs with you around to supervise and to give advice, like handling a checkbook, making appointments, getting a job, ect. Once she gains confidence from those things then comes the deadline to move and she takes that step.
Now if she's uncooperative and refuses to follow house rules ect.......then that's not going to work and you'll probably have to use the sink or swim method.
Hugs.