Try keeping her learning on the hill until she is very sure of what you are asking her for, and gradually decrease the slope you are asking her to perform on if you can (I know it can be hard to find suitable hills for the little ones).
this is the link to the one i found http://welshcobshop.com/product/county-in-hand-cob-whip
but if you search 'cob in-hand whip' it seems like there are many places that sell them. most are in the UK, so not sure what shipping would be, and there are normally a few on eBay. This one is £17.50...
I'm very new here, and I'm more into showing, but I noticed many people were looking for a whip suitable for use with a Hyperbike.
We use these whips for in hand showing with bigger horses in the UK and was wondering if it is a good solution to the problem as it is short but has the lash on it?