My suggestion to you is: Let her count the puppies.
In my country, pre-K is 2-3 years old.
Are you using flash-cards that have pictures of the quantities on them?
For example: a flash card that has the number 4 with 4 puppies on it.
I encourage you to let her count the puppies. Use a different object on each card, let her temporarily associate the number 4 with "4 puppies", and 5 with "5 flowers". Encourage her to count the objects instead of guessing.
Early on, children will associate the strange symbols we use for letters and numerals with practical items, hieroglyphs if you will. Most children will begin to learn by saying the alphabet, or counting (saying the numbers they know). Counting to 10 or saying the Alphabet begins for children much like singing a song or rehearsing a poem.
Later, children will use their "number song" to count objects. Later still, they will associate the obscure symbols we use for numeral indication with quantities. This is the goal you are trying to achieve. I would take a step back and allow her to count items on the card, and she will begin to associate the 4 puppies she counted with the symbol "4" she has no prior experience with.
This is the same way children learn their letters, which is not the same as learning to read.
Children learn different things at different rates. Her brain might not be ready to associate these abstract symbols with words (the verbal number). I am not saying it cannot be taught with repetition, but her age may be an obstacle at this point.
Similar phenomena exists when attempting to teach things like the concept of pointers in computer programming. Without building blocks it is difficult (but not impossible) to get these new concepts learned.