Hi K..
I know it is challenging and stressful. And yes, the timer sounds like a great idea because you DO need not only to have boundaries, but to make her aware of what they are, so she can learn self-control.
BUT, consider also, that this could largely be a function of her personality. All children (people in general) have their own unique personalities, but there are some generalizations that can be made. She is probably just more outgoing, gregarious/ extroverted. Some kids are more shy and introverted. She sounds like an extrovert. There is nothing wrong with that and you can't change her innate personality. Figuring out a method that works for you both to manage your time is another matter. But the fact that she craves your attention for play time isn't a sign that you are doing something "wrong"... or failing at something...
My son was a HANDFUL when he was small and ALWAYS needed my attention to play. It was very hard for him to stay entertained alone. My daughter, 3 yrs behind him, is the opposite, much easier to "manage" and more shy and quiet. These days (he is 11 yrs and she is 8) he can play alone VERY easily... but his preference is still to find his sister to play something. And he makes friends EVERYWHERE he goes.. and I mean EVERYWHERE, and not always the same age as himself! Changing schools (which he has done several times) has never been as stressful for him as it might have been for some other kids... because he just makes friends that fast...
My daughter, on the other hand, is perfectly content to play alone, quietly for HOURS... she will allow him to drag her outside to play.. but she usually makes him compromise in some way b/c the social aspect is just less important to her. She is a little shy around new faces, but eventually warms up. It usually takes half the year before her teachers at school see even an inkling of her true personality. She has plenty of friends too, but she takes a little longer and is more selective about the whole process.
So, while I know it is very hard right now, celebrate this extrovertedness in your daughter. It is just a sign of her personality. She will probably be the kid at school that always has lots of friends around her. You probably won't have to worry about her sitting home alone later on... she'll be out doing things with her friends!