I say do it.
Our puppy was sick when we got her (breeder paid all bills to get her well, but it was an eye-opener to the costs of vet emergencies). So we got her insurance right away.
She is only 9 months old now and we have used her pet insurance 3 times now (she is a bully, so had her nose done-to enlarge the nostrils for better breathing, she hurt her leg, & had a hotspot on her face which required antibiotic). All 3 times, 90% covered, simple process, and don't know what we would have done without the coverage after seeing the full bill amounts. We are actually ahead of the game $ wise.
We went with TruPanion. I researched all the top companies, checked Better Business Bureau ratings, made a spreadsheet and everything. With TruP. we were able to add a hip displaysia rider (most do not, and with bullys this can be a common problem) we have a $0 deductible (we were able to choose our deductible, which in turn adjusts the monthly premium) and they pay 90% vs others which are usually 80%. It costs us $40/month.
And we had her nose done same time as her spaying, so she would only be under once, and TruP covered the anethesia - which they didn't have to.
Best $ we ever spent. In fact, her leg is still not healed and may need x-rays, which will be covered.
I submit the claim, receive an email when it's been approved, and I have reimbursement check in hand about 7-10 days later.
Only things not covered are her annual exams and yearly shots (and spaying wasn't covered) - but we were good with that because these are costs we expect to have. We just wanted some peace of mind for the unexpected, and let me tell you, we are so glad we did it.
Some companies you can purchase insurance for the routine items too, but that wasn't necessary for us.
Do your research, check out their websites, check BBB, make some phone calls, and you will find one that fits the needs of you and your pet.
PS I do not work for a vet or a pet insurance company. I am in finance so I am very analytical, hence the research I did
HTH