My guess is that it was marked wrong more for the use of "one" instead of "a", as opposed to the placement of "only." When people say "just a minute," they don't mean precisely ONE minute; they simply mean a short amount of time. In addition, while your placement of "only" may be the correct one, that's not how most people talk.
According to the RAE, Real Academia Española, it is recommended that we utilize "solo" in every situation, even in the situations where ambiguity is present. Source: http://www.rae.es/consultas/el-adverbio-solo-y-los-pronombres-demostrativos-sin-tilde
Why is "solo" the first word in the sentence.
I understand that adverbs are often placed immediately before the verb. But this is not the adverbial form because there is no accent. So, it must modify a noun. There are just two nouns in the sentence--"we" and "minute".
"Only we" is unlikely because the meaning of such a phrase would be "just we have a minute".
So, "solo" must be modifying "minute"--"just a minute".
That makes more sense.
BUT why is "solo" at the other end of the sentence from the word it modifies?
Why not "Tenemos un solo minuto."?
You can say either "Solo tenemos un minuto" or "Tenemos solo un minuto", it doesn't make a difference. The former version just sounds better, just like "We only have a minute" sounds better than "We have only a minute." Or at least those versions are used more frequently.
If you want to say "Only we have ...", you need to include the subject pronoun, since that is being focused on now: "Solo nosotros tenemos ..."
I am learning my third language, using my second language, English. When I forget a small letter as the last "e" in "minute", i find it to be sooo annoying and demotivating.
Really, Duolingo? I understood the spanish sentence perfectly, but wrote the English "minute" without the "e", and you mark it as wrong?