Your premise is spot-on, if pretty common in fluffy writing. Every author does the little things a bit differently, but as a general rule, fluffies never refer to themselves with first-person pronouns like “I” or “me” and will use their name instead (“Bubbwegum wub dem names, Daddeh”). There are other nuances to it (broken grammar, inability to correctly pronounce a wide variety of sounds (“wub” instead of “love”)), but that and tawking wike dis are the main things you should keep in mind.
If you want your fluffspeak to be more accurate, study the fluffy dialogue in other stories and refer to Fey’s Fluffspeak Primer and the other FAQ pages when writing your own. Keep up the good work!