I recently had to look for various diminutives from latin words, however I got stuck when I had to find the diminutive for "Insula". After many researches on the Internet I came across some ideas such as "Insulitta" (but I think the "-ittus, -itta" suffix is only used for proper nouns) or "Insulla/Insella". But I can't find any informations about the diminutive of insula, so I'm not sure it is the right way to write it...
Cassell's Latin Dictionary translates the English word "islet" to Latin as parva insula.
The Dictionary of Medieval Latin from British Sources (DMLBS) contains the word insuleta / insuletta, defined as "islet, small island". ( https://logeion.uchicago.edu/insuleta ) But this is not attested until the 13th century (so the late medieval period).
As you mentioned, -ula is a diminutive suffix. Lewis & Short's Latin Dictionary actually contains insulula but dismisses it as simply a "false reading for insula".
Not all words have attested diminutive forms. And while there are patterns to forming diminutives, they are only simple for some types of words.
Many Latin nouns ending in -ula were diminutives themselves; but not all (it doesn't seem to be the case for insula). Words ending in -ula sometimes had diminutives where -ula is replaced with -ella, as in fistella from fistula and sitella from situla. There are also diminutives ending in -illa, such as papilla from papula and maxilla from mala.
Diminutives did not commonly end in -ulla. (It looks like there might be a few possible examples.)
So in theory, either insella or insilla look like plausible or reasonable diminutives formed from insula, but I don't know of any evidence that they have ever been used (so I wouldn't recommend using them yourself).
I found a passage from 1843 that claims that "Insilla est diminutivum ab insula, et dicitur parva insula."