It depends on what you mean by 'experience'. I think the other answers in this thread are thinking in terms of an organised day run by the Zoo.
On the other hand I wonder if you just mean a good day out with your daughter to give her positive experiences of the animals. If so, I would recommend Bristol, which is very child-oriented these days. It's not too very big and it has a nice range of animals, including lions, gorillas, meerkats, snakes & crocodiles - plus penguins and a breeding group of fur seals (a little smaller than sea lions but otherwise no different). There are regular animal shows on the lawn, a play area and lots of children around. I think it would be your best choice if you were on holiday nearby.
I think Blackpool would be almost as suitable. It's a bigger area, but has much the same animals plus elephants and one or two more. It has a huge sea lion pool and there is seating beside the pool to watch the shows at feeding times. It also has a playground, a miniature railway and a children's farm with strokable animals.
Hope this helps
Alan
