Your daughter deliberately used a slur towards your brother, that she knew would cause the most upset. At 11, she doesn't have the understanding of false accusations, how those accusations can destroy a person's life, that historically the gay community have had to deal with hatred or a proper understanding of the word she used. She does though know right from wrong.
Is it possible OP, that she's seen the news in more recent months, where a gay couple adopted a very young child, and abused him? It's possible something like this has made her believe that all gay men are like this?
Your brother has every right to be angry. He's probably had to deal with prejudice and homophobic behaviour from complete strangers. To then have something like that thrown at him by his niece, who he adores, must have very much upset him.
Yes, you need a conversation with her. You need to explain the seriousness of accusations etc. I think you do need to explore where she got the idea, that gay men 'like little boys' from. Yes, children do use the word 'pedo' and thrown it around the playground amongst themselves, because they find it amusing. Again, it's a word used, where they don't always fully grasp the understanding of.
Your daughter needs to apologise to your brother. She also needs to understand that the consequence of her behaviour, is that he no longer wishes to look after her again. I don't think your brother is being unreasonable either. Yes, he is an adult, and she's a child, but that isn't an excuse. She's old enough to understand right from wrong and she knew the words coming out her mouth were wrong, and designed to hurt... otherwise she wouldn't have said them!