But that's also questionable because Darkspawn don't reach Lothering for some time. So we don't need Flemeth for general travel. There's nothing stopping us from heading North.
As we leave Lothering heading north we are attacked by bounty hunters. My best assumption is we would face that the whole way north with little to no supplies or resources. In the end everyone would leave you at the departure from Lothering ad you would be pretty screwed all alone with no help or resources to flee the country. Morrigan along with Barkspawn, Alistair and Leliana would all go to Redcliffe, because they all understand the significance of what's happening. Lothering is barebones and probably wouldn't afford the best source of supplies for the long travel north. As such you logically would probably travel to Redcliffe with them to gather your needed supplies and equipment. From that point you would encounter that whole crisis and yes you could probably still run, but how long before it would all catch up to you.
Now lets break down these choices for the difference races and backgrounds.
Human Noble: Due to your connection with this land and obligations to protect your lands and avenge your family you will probably stay and help Alistair + crew.
Human/Elf Mage: You naturally wouldn't return to the tower for fear of being attacked, along your way you will probably encounter those that will try to kill you because of what you are and if not them maybe the templars. Fleeing will be difficult.
Dalish Elf: Aside from fearful humans trying to kill you, you would be an outcast everywhere you went and stick out like a sore thumb for bounty hunters. You might try to return to your clan, but they probably fled north as well to avoid the darkspawn.
City Elf: As with the Dalish you would stick out and be a target for the bounty hunters every step of the way. Plus people tend not to trust the elves as has been proven.
Dwarf Noble: If you fled to Orzammar you would be killed on sight.
Dwarf Commoner: Killed on sight in Orzammar