I wouldn't say "without a problem." Generally, Disney is very generous about those things, though more recently we've seen more strongly-worded notations in the menus ("for our guests under age 10 only" or something like that) and there have been occasional reports that indicate that tolerance for the practice is on the decline.
Regardless, it is appropriate when a teen or adult orders off the child menu, to tip the server based on an adult menu item price, not based on the child menu item price.
Disney's table-service restaurant chefs are incredibly accommodating when it comes to personal preferences regarding food. They'll work with you to come up with a meal that you'll enjoy, even if you're the pickiest eater.