I have a girl I want to make a cake for, but because of her allergies, I don't know if it is possible. She is allergic to sugar, dairy (eggs are okay) and gluten. Any recipes or suggestions?
Allergies and the reactions can be quite different.
Is this a "could get bellyache" or "could die" situation? Single allergy (gluten or dairy) is mostly the first case, the combination could mean the worst case situation (think severe peanut allergy). Ask the girl and decide than if you still want to do it.
Is this a friend, a family member...?
Depending how severe this girl's allergies are, is the solution easier or more complicated. You can use gluten free flour (this girl will have it at home), perhaps use fructose or honey instead of sugar and soy milk and similar substitutes instead of dairy. You can find vegetable whipping cream. It would probably mean a "buttercream design" cake, because I am not aware you could make fondant with such restrictions.
But be aware that finding the right recipe is not the end of the problems. Your kitchen is not set as "gluten free, sugar free, dairy free".
If it is good friend or family, best solution would be to make the cake in her home, in her kitchen. Sometimes even trace amounts can be big problems - my brother almost died because of his banana allergy, because my mother bought him not prepackaged lemon ice-cream. Don't ask me how the banana traces got in it.
If you are still sure you want to do it, I can send you some recipes.
If you want to do it at home - either run all your bowls, spoons etc. through the dishwasher again and let it air dry or wash it and dry with new (meaning fresh) towel. Clean your countertops with paper towel or new washcloath.
It can be done, but there is reason why such cake would be very expensive. And it has nothing (or not much) to do with the price of the ingredients.