Your flower does not seem to have bloomed yet, but it does look like a female flower with ovaries below the petals.

Yup. Female flowers have the bulge behind the actual flower that will become the fruit. Male flowers will be a straight stem right up until it opens into the actual flower itself.

Thank you for the information. So is it strange that the plants already have flowers considering they are not very big in size? My watermelon plants are much bigger but have not grown any flowers yet.

Yeah, it is actually. You may want to pinch that flower off. If it gets pollinated, odds are the plant will produce a melon for you, but it'll have to put everything it's got into that one melon. Pinch it now, let the plant grow bigger, and it'll be able to support more fruit later.