I'm struggling to understand why if both of you are working full time, how you cannot afford to move, are you in debt? If so have you looking into debt management plans? Step change is the one I recommend to my clients.
As much as I don't like the idea of you re-honing your pets, it could be a option, the average cost of a dog is roughly £1500 per year, A cat is roughly £900 per year, thats not just pennies, it's a substantial amount that could be saved in getting your child her own bedroom!
Housing, you're not over crowded as you have a living room,! Could you sleep in the living room, or you in the smaller room and divide the bigger bedroom, as something is better than nothing!
There is also national government schemes out there also that can help people move, Help to Buy is one of them.
if your on a low budget and meet criteria you could also apply for a loan with 0% intreast
Have you looked into cheaper options in your utility bills, (smart meter) TV package, food bills, car insurance, look into buying a cheaper car to run etc...
Their is always options, explore them you will be suprised at the results.