I don't think they will do an antibodies test on the NHS just to make sure, it costs money.
If she doesn't remember then most likely you didn't have it, or you had it when you were very small (the younger you are the mildest the illness is) or you had it and went undetected, apparently sometimes it can be just a couple of spots and can be missed.
Anyway, if you have had it or not, it doesn't matter, you can still have the jab anyway.
I had my jab in Boots recently, because as far as I know I haven't had chickenpox and with a DD (now 2) I would be more at risk of getting it and it is horrible in adults.
I am considering vaccinating my DD too. I got the jab myself as the illness is really bad in adults but quite mild for kids, I even asked our GP what was her opinion about getting my DD vaccinated but she said she wouldn't do it (not that it was bad, just not necessary). I still think I will do it at some point, maybe when she is 3 or so...
However, I think that if your toddler is already vaccinated your risk of contracting the illness is small (unless you have a lot of contact with other kids, work in a health centre/hospital facing patients...)