For the very definition of a showbiz trouper, look no further than “Wait for Your Laugh,” a vibrant biographical documentary about one of the iron ladies of entertainment, Rose Marie. She had her own NBC radio show at age 5, billed as “Baby Rose Marie.” Now 94, she’d still like to be working. That’s tenacity.

Though she uses a wheelchair now, she is still full of pizzazz, and seems to be enjoying herself tremendously as she narrates her many decades of going on with the show. She’s a tough cookie, a survivor and a compulsive entertainer — she can’t help it, and the attitude is infectious.

She was born in Manhattan as Rose Marie Mazzetta, the illegitimate child of a father who didn’t always tread on the right side of the law and exploited her singing and dancing talents for profit. In the film, she’s quite open about the venerable connection between the entertainment business and the gangster world. She apparently was a favorite of Al Capone, recounting that he told her to call him “Uncle Al.” She also worked for Bugsy Siegel in the early days of Las Vegas.

Rose Marie had the moxie and drive to sidestep the ills that have blighted so many child stars. Later in life she became a successful nightclub singer and found she had a knack for comedy, which she cultivated. Her work caught the attention of Phil Silvers, who invited her to Broadway to appear with him in “Top Banana.”

Just as she avoided the perils of early stardom, she also avoided the kind of marital woes common in the entertainment industry. She was happily wedded to musician Bobby Guy, who died at a relatively young age — though not before the couple had a daughter, who shares some of her recollections of her mom. After Guy’s death, Rose Marie always wore a black bow in her hair while performing and still does to this day.

She was in a few movies, but it was on TV that Rose Marie won her broadest audiences. She hit the mother lode in 1961 in “The Dick Van Dyke Show,” as wisecracking Sally Rogers, one of a trio of fictional comedy writers, along with Van Dyke and her old pal Morey Amsterdam. Both Van Dyke and the show’s creator, Carl Reiner, appear onscreen to talk up her talents. For her part, Rose Marie was dismayed to find the show increasingly emphasizing its star’s domestic life (and the role played by Mary Tyler Moore as his character’s wife) over his work world.

When the Van Dyke show was canceled, she found a nice niche on a game show, “The Hollywood Squares,” where her comic talents fit in perfectly for 14 years. Peter Marshall, the show’s host, gets a lot of camera time to recount fond memories.

Rose Marie also discusses her late ’70s venture, “4 Girls 4,” in which she toured the country with three other veteran female singers: Rosemary Clooney, Margaret Whiting and Helen O’Connell, the last of whom, she says, was a royal pain.

The movie apparently was made with a limited budget, but director Jason Wise clearly set out to create a bouquet for Rose Marie, and his affection shines brightly. He uses some nice home movies and photos provided by his subject, but you’re likely to end up wishing there was more performance footage. There are also a few short re-creations that are something of a letdown.

But these are quibbles. On the whole, “Wait for Your Laugh” is a well-deserved and most enjoyable tribute to a great entertainer of the old school.

Walter Addiego is a San Francisco Chronicle staff writer. Email: waddiego@sfchronicle.com.