if you go to the souk they have great jewellers there, not so expencive as the ones in al sadd street.
you can go to the shops near/behind Al Fardan Exchange.
Also if you have any old jewelery that you dont use you can exchange it there.
maybe have the ring engraved to make it more personal, it can be better than expencive. woman always appreciated personal touch.
Good luck And hope you find something lovely.
And congratulations :)