You are liable for the in the vehicle, because the title is still in your name, the plates are yours and so is the insurance or still in effect (I would leave a day or two of coverage past the sale just in case for CYA, screw the refund chump change for extra risk safety ). A lot to gamble if you don't know and trust this person. Surely someone she knows can help her, after all she is getting ride down with someone who can follow her back and two people with backing stories on the side of the road, most LEO would cut them a break for a vehicle transfer of ownership. Even the LEOs who are "performance reviewed" for amount of "paperwork". There are enough real issues that they don't need to make case that will get thrown out.
Question why can't she bring down a friend's plate or have an insurance binder for coverage and show it if stopped with the just dated,signed and notarized(which is dated also) title, I image most LEO would give them a break with at most a warning ticket but likely a verbal "make sure you get it done ASAP". Even if she did get a ticket, all it would take is "D.A. i had just bought the car, had insurance and was not able to get a tag for car i did not own which see here i did all of this the next day at the DMV when they were open". Pretty much not worth the hassle and getting legal gets tickets dropped normally, so the odds are.... . Insurance coverage can be binding on transfers but they have to pay and you can even float in there if you crooked/gamble with a policy that doesn't have the license plate tied to it but the make and model plus year. All shows intent, the DMV is not 24/7 and people have lives. This person may be 100% legit and doing everything they can and will do as said, which makes the caution seem foolish but getting burned is far worse.
I would make sure you had yourself covered because what if that title doesn't get registered? Then you are still the owner for liability(you can prove you're not in court but what will that cost you....), taxes and the state , county, and city will want their share. They can be reasonable and total understanding. Totaled a vehicle and did the dispute over owing any such tax, and especially of a high amount(other scrap value in theory) and it was in transfer to the insurance company for ownership during the change over for the tax ownership date. Which was set a letter saying i was released from any debt and owed nothing. So the Tax people are really decent and will work with you, if you show them proof. Since you are having to have it notarized, have her sign it there also and photo copy it for you records. But do not let them go with your tags, that is risking troubles. A title with just your signature is a gamble make sure they fill in their info in front of you. if you can't photocopy/scan it take a photo and even offer to take one with your phone of her with it and send it to her her phone(creates a trail & protection for you)
Stolen tags have values especially if your vehicle is popular model and color. Automatic Tag readers and their updated software databases can take time for entry and for data population to all users. If such officers even have the equipment. Now add an out of state use in the mix and things get even more sketchy ....
Sadly we all have become paranoid because of scammers. remember when certified checks and money orders were all good to go? Sad how far the criminal element has ruined trust and goodwill of people.
The LEO forum may give you better answers for advice and warnings.