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'.

Dollop is definitely a reasonable answer if you want less than a "normal" amount of cream on your strawberries, especially compared to "oodles" or "lashings" (which both imply you want a lot more than would be normal).

A dash is a reasonable amount for hot sauce, a spice, or maybe sugar with strawberries.

But for cream + strawberries, a dash would be too little and maybe nearly pointless. You'd barely taste it, like maybe be enough to get a few of them damp. That seems nearly pointless to me; if you don't like cream then just ask to not have any, but I'm lucky that I don't have to mess around with tiny servings to stay healthy. Maybe you could get some flavour out of a dash of cream on a couple strawberries. (And I like milk, cream, and dairy in general, so maybe I'm just having a hard time imagining liking only a small amount of cream more.)

Of course, given that we're talking about cream, you'd probably end up with an amount at the lower end of what's reasonable, rather than any specific quantity like 1/8th of a teaspoon. i.e. "a dash of cream" will be lot more volume than "a dash of hot sauce" when you're talking to another human, not a robot strictly applying a definition of a dash.

So on second though, a dash is a reasonable answer, too.

A dollop could definitely imply you want less than is normally served, but it's pretty subjective so you'd probably want to say "only a dollop" to get about enough cream to get the strawberries wet but not have much excess liquid in your bowl.

This answer doesn't really have a strong point one way or the other, but hopefully it gives some insight into the subjective implications of the words. Or makes you want some berries + cream. Going to get some now (blueberries + raspberries).