Well there is a plethera of different types of fungi of course but VERY few represent any real threat. The mushroom as you may know is just the reproductive body of the fungi and the actual fungi is growing in the soil, or in some cases wood. The ID of gilled fungi is ofetn difficult by a pic but if you want to take a pic we will give it a try. In general americans (and british) are absurd about the dangers involved with mushrooms. Some are dangerous to be sure but then again so are MANY plants yet we dont fear our garden. Fungi and important to the health and well being of plants and soil, they also are important recyclers. So go forth enjoy your fruiting fungal body and enjoy. Good luck.

Its what we refer to as a LBM (Little Brown Mushroom). In other words I have no idea, there are hundreds of little guys that look like your pic. If you have iterest in persuing this further you need to do a spore print so we know what color they are (an important first step in ID a fungi). But all in all I dont think this fungi represents a threat to you, your plant, or cat. Good luck.