The sentence is correct as it is. With "to", it would also be correct but would make a little less sense.
Short version: There are two "dares", a modal verb and one is a main verb, and they're subtly different.
Long version: "Dare" seems either has been in a state of flux or been two different verbs for a while. It's been hovering since as far as back as Google Books records go in the 19th century. As a reminder, modal verbs include "he will go"; "she must sing"; "he can fly" – all of these lack "to".
"Dare" can certainly appear without "to" as well. Here are some correct phrases where it does:
You dare speak with me?
You wouldn't dare.
I don't dare go without you.
However, while none of these sound wrong, they all sound a little more archaic or poetic. One exception is "say", which is by far the most common — and for some reason has consistently dominated the version with "to". It's actually so common that we have a fixed expression that you could nevertheless hear any day of the week:
This is the richest and, dare I say, the best cake I've ever tasted.
Note that neither one is more formal or informal. Although the above examples are poetic, you can also find "dare to" in poetry. For example, here's a famous line from T.S. Eliot's "The Love Song of J. Alfred Prufrock":
Shall I part my hair behind? Do I dare to eat a peach?
There's also a subtle difference in meaning, or at least in emphasis.
The modal "dare" seems to focus on the fear. For that reason it tends to occur in negatives and questions (NPI-permitting scenarios), which I just noticed all my three examples are. (Maybe "dare say" being so common is because it managed to hold on in a positive sense.)
This modal sense is the one Kevin's referring to in Home Alone: the robbers are so scared of him that they wouldn't dare mess with him.
On the other hand, the non-modal "dare" is less about fear and more about rashness, bravery, challenging fate. Somebody who "dares to dream" is a brave or rash person who overcomes the odds. And it's the same emphasis when kids use the transitive version: "I dare you to lick the ground!" or "I dare you to say that to her face!"
We also have the word "daring", which refers to this sense of "dare" — it means courage or courageous.
Hence, we can also read Eliot's "dare to eat a peach" as a proposal of a bravery: "Do I take this risk?" (The irony being that at Prufrock's frail age, eating a peach requires bravery.)