Yes. And it's Genitive here.
"fifty dresses" is one noun phrase, so you should treat it as a whole. If you just consider this noun phrase without any context, simply as a phrase, you will see that the numeral "pięćdziesiąt" takes Genitive. Just like most other numerals and other verbs denoting quantity.
"mieć" of course takes Accusative, so now you have to figure what's the Accusative form of the noun phrase "pięćdziesiąt sukienek". Luckily it's the same as Nominative. And then you arrive at "Ona ma pięćdziesiąt sukienek".
Most numerals. Some take Nominative. Those are: 1, 2, 3, 4 and those ending with -dwa, -trzy, -cztery (therefore not those ending with -12, -13, -14).
The others take Genitive.
And then you have special forms for 'masculine personal plural' and those take Genitive as well no matter what the number is (well, apart from 1).