Hi Gabriela!
Thank you for bringing your question to the Disney Parks Moms Panel.
Fantasmic! is one of my favorite shows, so I completely understand why you'd want to squeeze it in to your upcoming Walt Disney World trip!
While times are subject to change,
Mickey's Backyard BBQ begins at 5:30 PM and lasts for about an hour and a half. This would have you rounding up and out of there around 7 PM. Fantasmic! at Disney Hollywood Studios starts at 9 PM. I'd give yourself at least an hour to get to
Disney's Hollywood Studios which would put you there right around 8 PM. If you enter the park and immediately head to the Fantasmic! area I think you should certainly make it in time! You may feel slightly rushed, but I don't see why you wouldn't be able to make it.
If you are at all weary about the close connection, I'd recommend potentially catching an Uber between
Disney's Wilderness Lodge and Disney's Hollywood Studios. I find any Uber ride on property to be around $7-$15 and you'll save yourself time of having to wait for a bus. I don't think this is a necessity by any means, but if you'd like a better seat for the show, this is probably a good way to guarantee that!
I hope you have a magical trip and please let us know if you have any other questions!
-Lindsey ºOº