Hitting a rough patch and taking a break after three months seems incredibly soon. At this point you should still be getting to know one another and falling for each other, and if you're already getting on each other's nerves that isn't a good sign.
Taking a break isn't a good idea, as it allows you both to go and do things with other people, which inevitably leads to jealously and insecurity. If you're having issues then maturely and calmly talk things through with her, and maybe give each other a bit of space for a while.
But unless you're okay with the idea of her sleeping with other people, a break isn't good for a relationship, especially one as new as yours.