Doable, but difficult. I've long thought of a scenario I would have written into a TL after my Alyaska TL where this happens, and this begin by killing Koxinga off before he gets to invade Formosa (then the name of Taiwan). This would avoid his invasion and the Qings' thereafter, since they invaded to suppress the last bastion of former Ming loyalists.
So far, Formosa hadn't been considered more than a piece of mud and not worth a conquest.
Then, Dutch control won't probably be challenged until the 18th century when the Qing dynasty began clamping down on foreign trade and restricted it to Canton. A Dutch outpost so close to the coast of Fujian and harboring smugglers could be a tempting target. I don't know how advanced was the Qing navy in the 18th century, but given the Netherlands were mostly at peace until the late 18th century, they could have mustered and focus their naval power to defend Formosa.
At this point, Formosa would be probably one of the Dutch jewels of the crown since it pretty much acts as the VOC point of entry on the Chinese and Japanese markets, providing also tea and sugar from its plantation, plus minerals to exchange with Chinese merchants. Being so valuable, the British will no doubt try to conquer it like they did with Cape Colony, Ceylon, or when they invaded the Dutch East Indies. Would the Dutch be able to defend it ? Would the British return it to the Dutch in 1814?
Hard to know, even though it will probably be harder than seizing Java, since Formosa is much farther away from British bases then Java was, and they don't have Singapore or Hong Kong yet, but that doesn't mean they couldn't do it.
If Dutch Formosa makes it into the 19th century, I imagine it would separated from the administration of the East Indies (if it hasn't been done before).
Still assuming a minimal butterfly route, Formosa would unavoidably be occupied by the Japanese during WW2, though there might be some interesting action here. Indeed, Formosa being Dutch held would add strategic depth to Allies' holdings in East Asia, to British positions in Hong Kong and Americans in the Philippines, so probably a different campaign, but different how, I don't see yet.
In cultural terms, Formosa will have a more pronounced Aboriginal culture (OTL, missionaries transcribed the language using latin script), not being dissolved into the Han Chinese population, though Chinese laborers will probably remain a significant portion of the island population to make up for labor shortages. Add to this mix a strong dose of European culture, and you'd have a Dutch version of Hong Kong or Singapore I imagine. Except that the Netherlands don't have to retrocede it to China.
Post WW2, the Dutch would probably have troubles with a communist insurgency like in British Malaya, not to mention refugees from the civil war (in my TL idea, I had Hainan filling for the OTL role of Taiwan as the holdout of KMT). But I think they might retain their colony after the loss of Indonesia.
Independence is still likely to happen down the road, perhaps like Suriname, perhaps in personal union with the Netherlands (imagining a large inflow of european settlers leaving Indonesia for Formosa and exerting political influence to that end).