You could, but in English that sounds more like presenting the hedgehog rather than simply telling of its existence in a location, as there is ... over here does. I don’t think Finnish makes a distinction between these two sentences though, so it should also be added.
(I am a native Finnish speaker)
The word order in Finnish is heavily theme-rheme oriented, i.e. first you say the topic and then something about it. The beginning täällä means: attention, there is something close to me, closer than by you or anyone else. After that I reveal what here is, a cute hedgehog.
The case system liberates the word order, so that the subject can be last in a sentence. To my understanding this is not possible in English, which has a very strict word order, where the subject must come before the verb. This creates a need for a formal or dummy subject "There is…". But perhaps there is another way to express this in English, I don't know.
It absolutely is proper English.
"There is a cute hedgehog," simply means that a cute hedgehog exists somewhere without giving any indication of where it is. To give the location, you can add a phrase such as "over here" or "over there" to the sentence.
If you say "Here is a cute hedgehog," it sounds like you're presenting a hedgehog or even offering a hedgehog. If you use another locative phrase, such as "over here" or "under the hedge" and then follow it with "... is a cute hedgehog" without "there", it is correct English, but it just sounds like fairy tale language.
The part "There is" is so called formal subject required by the English grammar plus the predicate, main verb. It does not denote any location. "Over here" denotes the location. See the comment by AGreatUserName which to my non-native English (I am a native Finnish speaker) ears sounds plausible.
You might also want to take a look at my article About the word order in Finnish here in Duolingo.
Basically all native speakers of modern English speak like that. As Juha said, the "there" in "there are/is/was/were/will be" (etc.) doesn't indicate any location.
"There's a dog." (No indication of location all all: A dog exists.)
"There's a dog here." (A dog exist and it is here.)
"There's a dog over there." (A dog exists and it is over there.)
Using "There is ... there" or "There are ... here" is perfectly normal and not redundant at all.