Yes, Diana is Artemis and Luna's daughter, but she is not the only other sentient cat. In addition to this trio:
in the original manga, Luna and Artemis are natives of the cat-themed planet Mau, which is in the same galaxy but is outside of the solar system (how this aligns with the cats serving Queen Serenity in the Moon Kingdom is not explained; apparently Luna and Artemis immigrated to the Moon at some point). Mau is the same planet that Sailor Tin Nyanko comes from. Sailor Tin Nyanko was not originally a real sailor soldier according to manga canon; rather, she killed the planet's true sailor guardian, Sailor Mau, in order to gain synthetic soldier abilities. All sailor soldiers and other special beings who likewise possess true star seeds (such as Tuxedo Kamen, Luna, Artemis, and Diana), who died by having their true star seeds removed, after Chaos was defeated, received their star seeds back and came back to life. Thus, living on Mau at the end of the manga series, there are 1) a resurrected Sailor Mau (implied to be humanoid, simply on the basis that all sailor soldiers we've met have been humanoid, but since she was not specifically shown or described beyond her name, it is not impossible that Sailor Mau could be a sentient cat herself... especially considering that Luna, Artemis, and Diana each have a humanoid form that they can transform into), 2) other humanoids (like Tin Nyanko), and 3) the implication of other sentient cats as the regular residents of the planet Mau.
(Diana is the only sentient cat who is not a native of Mau, since she was born on Earth in the 30th-century Crystal Tokyo.)
(Note that the Sera Myu musicals follow the manga with Tin Nyanko as Sailor Mau's assassin, but the anime canon differs, in which Sailor Tin Nyanko is a true sailor soldier who was originally good but got brainwashed by Sailor Galaxia's bracelets, and there is no mention of Mau or of Luna and Artemis' further backstory.)