No, the word 'wonderingly' is an adverb, a word used to modify a verb, an adjective, or another adverb.

The word 'wonderingly' is the adverb form of the adjective 'wondering', the present participle of the verb to wonder that functions as an adjective and a gerund (a verbal noun).

The word 'wonder' is both a verb and a noun.

A noun is a word for a person, a place, or a thing.

Examples:

She stared wonderingly at the scene trying to make sense of it. (adverb)

He was wondering if we were busy on Saturday. (verb)

His wondering eyes got wider and wider. (adjective)

You wasted a lot of time wondering instead of looking it up. (noun)

I wonder what time the movie starts. (verb)

It's a magical tale filled with wonder. (noun)