Yes, just like that Brandon died. It wasn't an instant death however, it was slow and painful, just.... not hugely significant to the story. It wasn't like he's been a main character for like three books, he was our hero's horse for five chapters.
Anyway, as Brandon was brutally mauled by the huge rabbit, something occurred to Tim:
"You there, on the rabbit! How would you like to go on an adventure with me and my friends?"
"His name is Brian!"
The lady replied, evidently annoyed that her 'Brian' had been called 'the rabbit'.
"However that is something I would like to do! I will join you as long as Brian gets to eat as many insignificant yet named characters as he wants!"
Tim nodded and went off to find a new horse at the stables, followed by his new group of friends: Lem, shrouded by his hood; The Haggis, perpetually eating his food of choice whilst balanced on his teetering, unstable horse Kyle who looked like he was about to collapse; and his three new aquaintances Brian, his owner and the Fedora-master.
After a few minutes of bartering Tim mounted his new, unnamed (and therefore inedible to Brian) horse. The rest of the group who did not yet have steeds proceeded to do the same, and the group left the town of Sheffield with three new members and three new horses.
After a few hours of travelling the band arrived at what appeared to be a tower in the middle of nowhere; hair draped from one of the windows, and this intrigued the hooded figure of Lem. He dismounted and strode up to the long, fine locks, evidently both intrigued and strangely attracted.
"Oi, u up in da towa! Wot u doin up der?"
A voice replied from within the highest room:
"I am trapped here, unable to get out! Inside the entrance is a furry, the likes of which you have never seen! Please, climb up my luscious locks and save me!"
Lem was clearly taken.
"Im cummin up! Giv mee a sec an il b der 2 sayv u!"