Yes. Females are always carrying eggs.
Daft though it seems, This simple question is actually very difficult and far from stupid, you can even make an argument that female axolotls never contain any eggs!
If you take the definition of an egg as what scientists call an ovum, a cell that has undergone its last division which reduces the number of chromosomes to half the number in most cells, and is capable of being fertilised, then this usually happens after the "egg" is laid and despite the mating dance and apparent internal fertilisation this last division and then fertilisation occurs after the "eggs" are laid.
So despite common sense saying the axolotl is laying eggs it is laying unfertilised oocytes covered in sperm, the oocytes become an ovum briefly outside the axolotl and then if fertilised becomes an embryo!
Females do carry egg precursor cells, oocytes, in their ovaries from before hatching until they are very old. If adult and well fed they usually have "eggs" pretty nearly ready to lay if given the stimulus of mating. If kept on limited rations or conditions are otherwise unsuitable they may not have any near mature oocytes. Feeding them up brings them into fertile shape.