I won't get in to the ethics of right to buy as, ultimately, the option is there and so, while it is, I don't blame people for using it, even though I appreciate the issues it causes to the housing stock as a whole. That is not OPs fault and if she didn't buy the property, someone else would.
Focussing on the practicalities, which is what OP wants to focus on, there are plenty of people that have families in a 1 bed flat. I had a member of staff that lived in a 1 bed flat with two children, though I really don't know how that worked!
If it's fairly large, does your bedroom have enough space for a full size child's bed and a double for you and your partner? If so, I think it's workable until the child is 5. They won't know any different and you can put them to bed and sneak in yourself later. Alternatively, you could turn your living room in to more of a studio with a bed and living room furniture so your DC could have your bedroom.
I definitely think it's feasible OP and agree with a PP about not delaying trying for a baby because of it. You don't realistically know how long it will take to conceive anyway. You may be lucky and get pregnant quickly, but if it takes a bit longer, then you might want to start the clock running.