I'm curious why you're asking. If you want her to do this, then why does your title question ask if you should "let" her? I get the feeling she doesn't want to drop out?
She's got a lot of growing up to do quickly, which means it might be easiest for you to set conditions under which she can live in your home with her baby. Then let her figure out how to manage this.
For example, it should not cost you more to have her there, meaning at a minimum she needs to cover her and the baby's food. Tell her she needs a plan for that. She can always take online courses, but this also costs money. Does she understand that her social life and "fun" spending will no longer be an option?
Finally, have you talked to her about adoption? If you hate the thought that a grandchild of yours wouldn't be a member of your family, this may not be fair to either the grandchild or your daughter. No baby wants to be born into a mess like this, especially with a deadbeat dad. And your daughter clearly is nowhere near ready to be a mom. It should be on the table as an option.