Ds1 (now 6) was like this. Started to walk day before his first birthday, started to run the next day and hasn't stopped... Even now it's difficult to get him to sit to do something (especially eat or calm down at bed time. Dread to think what he is like at school).
But he has got a bit better in that - if he is interested in something - he will now watch tv, even if he is usually bobbing around and doing other stuff concurrently. Wrestling his little brother, making shadow puppets, prowling around like one of the animals from deadly 60 along with scary growl to scare little brother or running around with blanket in lieu of superhero cape are current favourites... And did I mention the incessant talking to accompany it all?
Sorry this probably isn't helping is it? 
But it does get a bit better, persist with keeping tv for periods of time on in the hope that she will see something that catches her fancy and watch for a little longer each time. And having a toy and book that ties in with something she likes will all help, especially if she will play along. And now is a good time for her to be concentrating for longer and longer.
Also agree with asking nursery as they will have lots of other kids to compare her to. Used to pick up ds1 from nursey and they used to reckon that he was always on the go especially in the Sumer when they were out all day. But it all goes to helping them to sleep well which was a big help to my sanity.
You say your dd is sleeping well and otherwise happy so that has to be good. Can you have some strategies to direct her busy-ness so at least you have a little control, even if it's just moving her into a different room to play more ? Or asking her to do things like march over there or come back jumping as a frog or spend the next 3 mins being a caterpillar? Then you get to slip a few slower ones in
.
It was at this sort of age that ds started to love the Hoover, washing machine etc. I'm a slattern by nature 
but he adored using the real thing and even now as a special treat he is allowed to do some hoovering etc... childexploitation great win win situation and way for him to burn off energy.
At the end of the day though (sorry this is long, keep getting interrupted so have lost track a bit here) you know in your heart of hearts if you think she is fine and you have just got a very active dd or if you are worrying about something then ask your gp. And if you are worried about something in particular ask them to rule it out explicitly - unfortunately it seems to be the most successful tactic in these litigious times of getting them to take you seriously if they have to sign to something specific on your dd's notes.
Good luck and hope she learns to watch tv and give you more than a few moments break soon!