Attributive adjectives, i.e. those in front of the nouns they refer to, always get a proper ending/declension. It would be klein without an ending only if it would be a predicative adjective, that is an adjective connected by verb like ist/sind/wird, for example "Das Mädchen ist klein und spielt auf der Trommel, die groß ist". Regardless of the gender der/die/das.

In general auf is a two-way preposition that can be used with dative or accusative depending on the meaning. Accusative is a motion (onto the drum) while dative is a position (on [top of] the drum).

Have a look here: https://deutsch.lingolia.com/en/grammar/adjectives/declension

Das kleine Mädchen is the subject of the phrase, so it's in the nominative case, while "die große Trommel"(nominative) becomes an object in the dative case (due to the usage with "spielen auf") and turns to "auf der großen Trommel".