Car- is the Quenya verb for “do, make”, derived from the root √KAR of the same meaning, and was very well established in Tolkien’s mind. ᴱQ. karin “I do, make” dates back all the way to the Qenya Lexicon of the 1910s (QL/45), and appeared regularly in Tolkien’s writings thereafter. Tolkien frequently used car- in examples of conjugating basic verbs, so the inflections of car- are pretty representative of Tolkien’s evolving notations of the Quenya verb system.
The English verb “do” has many specialized functions, such as in the formation of questions like “do you want to go?”. Quenya car- does not share many of those functions. Quenya car- serves as a “generic action” verb, in some sense acting like verbal pronoun, which can be substituted for a more specific verb. For example, in phrases like A carnë ta yallë B (carnë) “A did that as / like B (did)” (PE17/74) or ecuva nin carë sa nöa “I may do that tomorrow” (VT49/20), the verb car- is a placeholder for the specific action done, in the same way that ta and sa is a pronominal placeholder for the action as a noun.
The English verb “do” often requires a generic object like “it”, but that is not the case for Quenya car-: consider English “don’t do it” [with object] vs. Quenya áva carë [without object] (WJ/371) or the Quenya phrase á carë ancárië “try harder” (PE17/94), more literally “✱do [it] with more doing”. When car- has a specific direct object, it generally has the sense “make” or “build”, as in ma caruvalwë ohta “shall we make war” (PE22/161) or i carir quettar ómainen “those who form [make] words with voices” (WJ/391).
Conceptual Development: In The Etymologies of the 1930s Tolkien had ᴹQ. karin “I make, build” under the root ᴹ√KAR {“make, do” >>} “make, build, construct” (Ety/KAR), and in this period kar- was more often glossed “make” rather than “do”, such as in the Quenya Verbal System (QVS) from 1948. It could be that in the 1930s and 40s this verb was more limited in sense than it was earlier and later.
An element meaning “action, doing, making” attested in words like lacarë “not-doing, inaction” (PE22/154), loicarë “mistaken action” (PE17/151), and saucarë “doing or making a thing very badly” (PE17/183), clearly based on √KAR “do, make”. It seems to be the infinitival form of the corresponding verb car-, but Tolkien stated in notes from the late 1960s that such a form was not infinitival when combined with other prefixes (PE22/154).
Conceptual Development: The English-Qenya Dictionary of the 1920s had the similar form ᴱQ. karo “act, action, deed” (PE15/68, 71), also mentioned in the Early Qenya Grammar with the gloss “deed” (PE14/45, 75).
Neo-Quenya: In theory the independent form carë could also be a noun meaning “action”, but more likely it is just the infinitive “to do, to make”, and the proper independent noun is carda “deed, ✱action”.