No. I know it seems like it should be, and, as an English speaker, it sure seems like putting in the word "ihr" (meaning the plural familiar form of "you") here is the natural and proper thing to do. Unfortunately, in this situation, it isn't. And the reason why is that the verb "danken" takes a dative object. That means whatever pronoun you do use after it (you, him, her, them, and so on) has to be the dative case version of the pronoun. As it turns out, the word "ihr" is the dative case version of the pronoun "sie" (her). The sentence you wrote actually means "I think her". The various versions of the sentence that mean "I thank you" are
Ich danke dir ("dir" is the dative case version of the word "du" -- you, familiar singular)
Ich danke euch ("euch" is the dative case version of the word "ihr" -- you, familiar plural)
Ich danke Ihnen ("Ihnen" is the dative case version of the word "Sie" -- you, formal singular)
[Note in the last example, the 'I' in the word "Ihnen" and the 'S' in the word "Sie" are both capitalized]
If you are new to German, or if Duolingo is your only brush with the language, I know this is extremely confusing. They don't do a good job of teaching grammar here. But there is a lot of information on this topic on the Internet. Try some of these links...
This Wikipedia article has a good table of the personal pronouns that show which version you use for a given "case" (nominative --> subject, accusative --> direct object, dative --> indirect object) http://en.wikipedia.org/wiki/German_pronouns
Also see this page, which summarizes the various forms of personal pronouns for the different cases. http://german.speak7.com/german_pronouns.htm
Keep on translating!
It's not as bad you think, the only dative (to form) that fits is the feminine singular form. Therefore it has to be "I thank her."
As someone else has pointed out, if it was the familiar singular dative, or formal singular dative then it would have been "Ich danke dir" or "Ich danke Ihnen" :-)
This doesn't look quite right to me. You need a version of "you" that's in the dative case, so "Ich danke dir" or "Ich danke Ihnen", or "Ich danke euch". Seems strange, right? The verb "danken" takes a dative object. I like to think of it as "I give thanks to you ". Easier to remember that way (for me at least).