I haven't grown melons in raised beds myself - not enough summer heat here for watermelon so close to the ocean :)

But most guides would discourage you from trying at a depth of 12-14". That would support shallow rooted plants while watermelon are considered deep rooted at 24-36" ideal. Try searching 'raised bed depth watermelon' and you'll find many examples like the following...

Here is a link that might be useful: One example, deep rooted plants in raised beds

Thanks for the link.

Will the raised bed have a bottom to it or will it be placed over existing soil? If there's no bottom to block them, the roots should grow into the original soil, giving you additional depth.