Could be a piece of food stuck on one of her back teeth, would explain why her breathing is unaffected yet she's gagging and unable to eat. It definitely needs sorting ASAP, she needs food going in her otherwise she will develop other problems. While she is unable to eat I would ordinarily suggest syringe feeding, however I would be in two minds about putting anything into her mouth before dislodging whatever is causing the problem. I suspect that she may be able to eat normally once the food (if it is that) is removed.
To be honest, unless someone else knows of a rodentologist or is able to use tools to access the back of the mouth, the only thing I feel is safe - and important - now is to go to the vet. Whatever is stuck needs removing, or she will unfortunately starve and risk serious digestive problems. Sorry to bring it back to that but it is the safest option for Little Gem.
Only other questions I have at the moment - you mention she is a new mum, when did she deliver her little ones? Is she otherwise well, aside from this gagging and inability to eat?