Getting a new queen is probably great advice by what you have told us here. It sounds to me as if she has NOT mated, which (for what ever reason) is not normal a week into her life. I was showing BigRog on Friday the qualities of a good prolific queen, here are a few to look for and if you lack any of these, chances are she's a dud!
A good mated queen (talking Italians here folks) take on a great translucient brownish abdomin, nearly stripless, quite long and with a healthy deep black thorax and "FULL" look about her over all size.
She should easily standout amoung workers, both in her unique look and in her general presense and movements. She should always be searching for cells to lay eggs in - typically she should be laying eggs at a rate of 2 to 3 a minute on a frame where cells are available for laying.
She should always have workers following her like the secret service follows the President. Most of these workers trailing her as she inspects and rejects cells to lay in. The trailing workers either study the cells to see WHY the queen refused to lay in it, or they communicate the need to other workers who will do the cleaning BEFORE the queen makes the next pass.
A healthy, prolific and strong pheromoned queen stands out in the hive, she weaves in and out of the other bees as if they are frozen in time and only she has the ability to move - rarely if ever does she stand still and only occasionally will you ever catch her feeding herself from an open cell of nectar.
Queens that are just present but not active as above are weak queens, either virgin or poorly scented for the role of queen in a hive. It is better to bring a NEW (unrelated) queen into the hive than it is to try and make a new one from this same hive - generally speaking, you can only create a queen of equil value to the failed queen you have now by raising another from the same hive.
Time is quickly running out for any egg laying, but if you hae a fairly sizable bee count in the hive, I wouldn't worry much about THAT issue. Requeening though will quickly regain the hive mentality needed for PROPER clustering - there is more that just balling up to keep warm all Winter, there is a technique about it, something driven by the pheromonal scent of the queen and without that, the bees have a very small chance of surviving the Winter.
Hope all that helps, but even if it seems too late to requeen for egg laying purposes, there are many more issues that are necessary for hive survival and requeening seems to be the best answer here.