I'm in need of some recommendations please.

Having spent the better part of this morning trying to take some photographs of my 16mth old daughter, I've come to realise that my 18-55mm el cheapo kit lens just isn't cutting the mustard .. for one thing, my daughter moves very fast so all I get most often is a blur, but she also moves around a lot (as children do) so my lens is always readjusting the focus and of course I've missed some potentially lovely shots.

I have NO IDEA really of what lens type might best suit in this situation, and I'm hesitant to visit my local camera store by virtue of them trying to sell me the most expensive glass they have that might or might not do the job I'm after IYKIWM.

So I'm asking the pros! If you can offer some advice by all means please do so