You will probably be better off saving money each month to put in your 'vet bills fund' and drawing on that when you have a medical expense (self-insurance). Otherwise you will make insurance premium payments on a regular basis and might find out later on that you get reimbursed little, if anything, when you have a medical claim. There are lots of ways to deny payment for your costs (pre-existing condition exclusions, limiting the medical conditions that are covered, excluding routine care, capping payments for a particular pet over a period of time - per year, for example; limiting the amount that will be paid over the pet's lifetime for a particular condition, etc. - the list of reasons not to pay you what you think you should get goes on and on).
Overall, insurance plans are designed to take in more than they pay out and pet insurance certainly follows the rule. (Although there's certainly nothing wrong with looking into it )
I checked into VPI- and teilbob is so right. You are much better off just setting aside some money every month and not going through an insurance. They are very expensive and the coverage is minimal with many exclusions. I keep an envelope in my monthly bill's file, and each month I put $5 or $10 in it, and it builds up pretty quickly. That way I always have money to put towards an unexpected vet visit.
I will look into VPI. After my bird Cookie was hospitalized for 4 days and the bill came out to be $1,000, I thought pet insurance might be worth it. But I guess I might be better off just saving some money every month to cover potential vet bills.
Pay particular attention to 'exclusions for preexisting conditions' - if that's a feature in the policy you are considering it means that the insurance will not cover any future treatment related to Cookie's medical problems known to date. So, for example, they will pay nothing towards your future expenses for her 'female problems'. Insurance companies do this because they know that a pet (or person) who has been diagnosed with a particular condition will likely need treatment in the future for that condition (as you would expect, right?). The 'preexisting condition' coverage exclusion, if part of the policy, is the excuse that will be used to pay you nothing for future medical treatment needed for currently known problems.
You can also check with the vet to see if they offer financing (payment over time) for expenses in the future - this, in combination with regular savings you accumulate in your 'vet bills fund', can help you manage unexpected high vet bills in emergencies so you're not hit as hard.
There's always care credit. Every vet I've worked for takes them. It's like a medical credit card, so you can use it for your dentist or eye doctor as well, but it gives you a limit and you can use that to pay for vet bills. You apply online and get instantly approved. I have it just for emergencies because you never know.