Yes, lots of people say the insurance company "denied the claim for no reason" but this is because they didn’t fully understand their policy which seems to be the biggest problem people have. You should really read the policy and understand what is and is not covered before signing up.

So it seems your dog is sort of accident-prone, so I’d definitely recommend pet insurance, especially because she is young — she has a whole life of possible accidents ahead of her. Obviously anything related to giardia, kennel cough, and future broken toenails will probably not be covered.

Though it’s kind of a lot of reading, this site has some really good information about what to look for in a plan: http://www.pet-insurance-university.com/pet_insurance_guide_lesson7.html

My own recommendation for a company is Trupanion. They have very few exclusions and limitations – no claim limits per year, per claim, or per incident, just a lifetime limit. Also they don’t exclude breeds or hereditary conditions — the only exclusion is hip dysplasia (which coverage has to be added on before the pet turns 1).
They cover 90% of the bill with no benefits schedules, and you can choose a $0 deductible which is what I would recommend.
Also there is no increase in premiums due to pet aging, so since your dog is young, you’d get locked in at the lower premium.
They cover conditions for life, so unlike some companies, they will not consider a condition preexisting just because your policy renewed.

In all, yes pet insurance is worth it if you know exactly what you are getting.
References :
http://www.trupanionpetinsurance.com

You do need one where the limit is quite high though and renewed yearly because operations and som treatments are way up in the thousands and will wipe out all your cover if you get a low one.
References :