Mine are now past this age but I'm of the hard core old school parenting style and I'd just say no!
Bikini's are a pita if you're diving into a pool, swimming, doing handstands on the beach, leaping over rock pools - the kind of things I expect an active 11 yo little girl to need a swim suit for. If you've got boobs you're mindful of them escaping and if you haven't you've got this thing riding up your chest.
At 11 a pretty crop top style with sporty shortie shorts or a fuller bottoms is ideal. You can find them with on trend patterns/detailing that go from aspiring Olympian to lazing on a tropical beach in style.
Girls and women are encouraged into these sedentary, posing and pouting roles often by the clothes they wear. High heels, short skirts, bodycon frocks, bikinis they're not designed for women who want to run, jump, climb,ride a bike, fly a kite, roll down a hill or wade through streams... the things I see 11 yo boys (often eagerly and energetically accompanied by their dads ) doing all the time.
Wearing what is essentially a bra and pants in public causes girls and women (subconsciously & consciously) to modify their movements to suit the constraints of the fabric. After all if you were happy to go nude, you would do but you're not so you've strapped three tiny triangles to your bits (hence the name of the company in OPs question)
I'm not bothered so much by what men or other people might think btw. Women have a right to dress how we want. If men/ others have an issue that's their problem to deal with so long as they don't act upon it and bother me or my child.
And yes there will be a time and a place in a woman's life when a padded pink neoprene bikini is a must have, to die for, fashion essential ..I've been there too... But an 11 year old isn't at that time and shouldn't really be at that place.
So own money or not .. it's a no from me and YANBU to not want her to buy it.