PEI was settled by Europeans beginning in the 1720's but didn't have a significant population (less than 5,000) when Louisbourg fell in 1758. When the British took over both Nova Scotia and PEI the island was governed as part of Nova Scotia. In 1765 Samuel Holland conducted detailed surveys of the island and carved it into 65 townships, or lots. In 1767 there was a lottery for the parcels and the land went to British military offers and other friends of the Crown. In 1769 the new landowners petitioned to set up their own government to protect their interests and PEI has been its own entity ever since.

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For it's size PEI had enough of a population and economy prior to Confederation to get its own seat at the table. Cape Breton was its own territory for a time but was annexed by Nova Scotia in 1820. To the best of my knowledge no province has ever tried to annex PEI, although there is occasional talk of merging PEI, Nova Scotia, and New Brunswick to form one province.

Originally, PEI (then called the Island of St. John) was administered as part of Nova Scotia by the colonial government in Halifax, but it became a separate colony in 1769 at the request of the land holders there (of which there were 17). These were people who had received land grants only a few years earlier (1767) and the first governor was Walter Patterson, a friend of the Earl of Hillsborough. The Earl was the President of the Board of Trade that oversaw the colonies and was partly responsible for appointing governors. Patterson had helped the Earl secure some large land holdings (60,000 acres) in New York and received a grant of 20,000 acres of his own on PEI.

In 1851, Nova Scotia had successfully pushed for "responsible government", devolving more powers from the governor (now Lt. Governor) to a legislative assembly, and the same model was applied on PEI. When Confederation rolled around in 1867, it was these legislative assemblies that decided on joining Canada. Nova Scotia did and PEI didn't, though six years later, the assembly on PEI changed its mind. Part of the reasoning was that Canada agreed to pay off debts that PEI had accumulated in building a railway system on the island, as well as buy out remaining absentee landlords on the island (the heirs of the original 17 landholders, who by and large did not live on PEI). At the time, the population difference wasn't as large - with PEI being about 40% of the population of Nova Scotia and a bit under 10% of Ontario (today PEI is about 15% of the population of Nova Scotia and just over 1% of Ontario). Manitoba, which joined Canada in 1870, and British Columbia, which joined Canada in 1871, both had a smaller population than PEI when they joined, so there was little precedent for PEI not being a province when it joined. In fact, Alberta and Saskathewan (which became provinces in 1905) both had smaller populations than PEI at the time they joined.

Since no one else has mentioned this yet:

It's worth pointing out that Nova Scotia, New Brunswick, and Prince Edward Island were, at one point, all one colony, then called Acadia (a part of New France). The Treaty of Utrecht ceded parts of mainland Acadia to the English, mainly Nova Scotia up to the marshes. New Brunswick was still French, but was contested territory; Prince Edward Island and Cape Breton remained under French control, relatively uncontested. It wasn't until the end of the Seven Years' war that the rest was ceded to the English (except St. Pierre and Miquelon) in the Treaty of Paris.

Cape Breton was made part of Nova Scotia, but Prince Edward Island remained a separate colony after that; I'm not 100% certain why, but I would guess that the distance by boat would be a big part of it. While not a great distance, it's much closer to go from mainland Nova Scotia to Cape Breton than it is to go from anywhere to PEI; this is only conjecture on my part, though.

Still, the separation of the colonies due to the battling between England and France, and the time and manner of secession, would have a great deal to do with it.