Are there Muslim restaurants available within Xiamen city?

Of course there are. And many of them are Lanzhou Hand-pulled Noodles Eateries. Here are two I know for your reference anyway:
1. Yilan Beef Hand-pulled Noodles at no. 9, East Xilin Road, Siming District.
2. Mohammedanlsm Style Restaurant, at the intersection of Lvling Road and Jinshan Road, Siming District. It is bigger and more popular, worth to go.
Or you can give me your location so that I can recommend you the nearby ones.