Is there such a thing as a proper verb, like a proper noun?
Solution 1:
The word "xeroxed" is an example of conversion. Conversion means the change of a word class without a change in form. It is very productive in English. For example, I can use the noun bottle and turn it into a verb he bottled the milk, or the adjective green and turn it into a noun we went out into the green, an ungradable adjective like English and turn it into a gradable adjective, he is very English, etc. In your case, you took a proper noun, Xerox, and turned it into a verb, to xerox. That does not make the resulting word a "proper verb", which is not even a recognized category in linguistics. It makes it a verb converted from a proper noun.
Solution 2:
No, there are not "proper verbs." There are verbs, which communicate an action, and then there's everything else.
Your example is not an instance of metonymy, as @user307254 suggested. Metonymy is a method of figuratively conflating one object or concept with the name of another, with which it is associated, for the purpose of metaphoric expression. To wit: saying "lay off the bottle" to mean "quit drinking" is metonymy.
What you have described is a phenomenon referred to as "anthimeria" by etymologists. It is sometimes colloquially termed "verbification," and it is a perfectly normal (and acceptable) aspect involved in the evolution of language. The process is not so much a problem of linguistics as it is a legal concern, resulting in so-called "genericide;" it primarily relates to intellectual property as it can result in the loss of trademark (Bayer lost its claim to the word Aspirin in 1921 due to generalized use of the word).
As a rule, the trademark will be capitalized, since it is a proper noun, whereas the verbal form with be lower case. You may have an account with Google, but you could just as easily use another search engine to google your query.
If it's listed in the dictionary as a verb, rather than slang, then it is as "proper" as any other. According to the three dictionaries I referenced (Merriam-Webster, Dictionary.com, and The Cambridge Dictionary of English), xerox is recognized as a verb, while Windex is not. An entry for windex was only included in the Urban Dictionary, suggesting that it is merely slang.
Thus to xerox is "proper," yet to windex is not.
Addendum
Since this answer appears to be mildly ambiguous, I will attempt to provide a laconic conclusion: no, there is not a verbal analogue to proper nouns.
Solution 3:
The Cambridge Dictionary gives the capitalised verb:
On the basis that dictionaries are authorities on whether a word is a word or not—at least for pedants—English does indeed appear to have proper verbs, so to speak.