At 11 months old, your child cannot be a brat. (And he sounds absolutely normal!)
I will give you my textbook statement regarding spoiling: When we do something for our child, at their insistence, that we do not want to do (and we often know is not the right thing for them), THAT is spoiling. Spoiling is often going against what one knows is right in order to appease a child, either because they are upset or threatening to be upset.
This would be the parent who buys the toy at the store because they want to avoid a tantrum, or the family that lets the child make the choices at inappropriate times because they want the child to be 'happy'. Spoiling comes from the habit of giving the parental power to the child.
With some babies, their opinions start to come to the fore, immediately. Their brains are still developing and often, they operate from their more primitive, 'lower' brain. Thus, any sense of disappointment or deprivation is perceived as pain, just as they would process having their fingers slammed in a door. It *is* real pain to them, and so we see their anger, rage, frustration and sadness.
What I would suggest is distraction and redirection, and setting up your home environment to provide as few 'no's as possible. I believe the last to be key. Some parents prefer not to childproof or change how they live to suit their child's immaturity, and prefer to 'teach' their child which things they might or might not have access to. I find that this doesn't really do a lot of 'teaching', because the child is often angry at being denied and doesn't absorb 'the lesson'. Instead, I find that putting adult things up out of reach is a huge help. Making their areas safe is vital to everyone's happiness.
Distracting/redirecting our children is also useful and works, even sometimes on adults! Instead of taking a toy away abruptly, draw your son's attention to something similarly interesting and gently say "Oh, this one (to be removed) is for mama. You may have *this one*" and hand it to him. Redirecting him when you set him down, making sure it's in a cozy place where he can move and has distractions (toys) helps.
I also found that it wasn't "no" that kids find so upsetting, but what *we* do along with that "no". If we are taking something away, or removing our child from something they are finding interesting, this can be what they are responding to. Over my years of working with very young children, I decided to stop saying 'no' and to just use positive redirection, mainly because "no" is both a trigger word and is abstract to a baby. Instead, I try to offer other toys in a calm way or to say "stop, please" or "let go, now"... telling the child what I want them to do. I've also found that this resulted in less automatic "no's" from the child during the toddler years, because I was teaching them a more effective way of communicating.
I found, too, that wearing my son in on my back at that age was a lifesaver for us. Babies need to be held, they desire contact, and become anxious when they feel ignored. If you can, consider wearing your little guy at certain times during the day when it's safe. Or put him up into the high chair, close by, when you are making dinner, so he can be up at your height. Let him keep busy with a couple of cheerios and practice his pincer grip.
Love your baby up as much as you can, and when he does get upset, try to remember that he's not a brat, he's just still very little. To learn more on human brain development, there's a great book called "The Science of Parenting" by Margo Sunderland which discusses the lofty concept in a very easy to read fashion. Even after years of caring for little ones, I found this book very insightful and informative in both knowing what our children are truly capable of feeling/doing and how to adjust my expectations and responses to best facilitate their healthy emotional development. Worth it!