What is the difference between "a dash" and "a dollop" of cream?

These are not precise measurements, so any answer will be subjective. First, I believe your title is incorrect -- this sentence is not referring to ice cream but (liquid) cream instead. The former is a frozen, generally solid dessert while the latter is a thick liquid.

So, in my mind, a dollop is like a heaping tablespoon of something while a dash is a few drops, much like the amount of hot sauce one might use if one didn't like spicy food. (This site defines a dash as 1/8 teaspoon.)

So, if you're putting cream on your berries, a dash isn't berry, er, I mean very much whereas a dollop makes more sense.

Note that the Oxford Dictionary directly contradicts the Cambridge, defining "dollop" as "A large, shapeless mass of something, especially soft food." (my emphasis). https://en.oxforddictionaries.com/definition/dollop

This corresponds to my idea of the meaning, as a native British English speaker, and obviously makes "dollop" the wrong answer in the OP's example.

A dash is two things, it is the action and it is the result of that action. Dash is an old word meaning a short, rapid action, used in sentences such as 'He dashed the plates off the table', meaning he violently swept them to the floor. With a liquid in a bottle, such as a vinegar bottle or a sauce bottle, the action of the rapid shake to dispense some of the contents was also a dash. What came out was also called a dash, meaning 'the amount dispensed by a dash of the bottle'.