We would not make the substitution; feta is likely to be much too salty. It is made in large blocks that are salted, sliced, salted again, then soaked for a month in brine. Some kinds of feta taste of little more than salt*. That’s not going to add substantially to your dish.
There are two perplexing issues in your question, though. Does the recipe really specify "goat cheese?" There are so many varieties of goat’s milk cheese it would be hard to suggest a substitute without knowing which variety is needed. Both flavor and melting characteristics can vary a lot. If it’s just "goat cheese," or one of the many varieties of chèvre, we’d look for a fresh cheese, such as farmer’s cheese.
Second, where do you live? Goat’s milk cheeses should be available pretty universally. If your supermarket doesn’t carry several varieties, there must be other sources available - specialty food stores, natural food stores, farmer’s markets, etc. If not, you should just move.
*Some - many - fetas are, of course, delicious. We do not mean to malign feta cheese in general, just those that are oversalted.