Howdy Richard! You are going to LOVE
Disney's Yacht Club Resort and your 11 month old will LOVE the sand bottom pool!
You can absolutely bring your baby tube in the big pool. In fact, I would encourage you to do so. We rented some items last year and while they were great for adults, the items didn't really work out for our little ones.
If you bring the tube, I would encourage you to keep an eye on it. We witnessed a few people taking tubes that weren't rented to them. It wasn't done maliciously. I just don't know that everyone knows that the tubes are rented by Guests.
Of course, your safety (and that of your little boy) are of the utmost importance to all of the Cast Members at Walt Disney World. As policies can change, I would encourage you to check with a lifeguard on duty before you and your son enter the larger pool with his tube.
I hope you enjoy every minute of your time at Disney's Yacht Club. We will be at the Beach Club Villas soon and I cannot wait to make a splash at Stormalong Bay!!
Thanks so much for your question and please let me know if you need anything further. Have a magical day!