I fully agree with xLeitix's answer in that you have nothing to be ashamed of in front of your supervisor - especially since she has already offered.
On the other hand, when talking about whether this will look desperate or impact your career prospects (in academia) negatively, I'd like to offer a different perspective from Anonymus Physicist's answer.
From my experience, and the experience of the people around me, what hurts your academic career the most is having a long period without a (research) position after your PhD. (But I've also noticed that nobody even notices short gaps of a couple of months). So while it would have been better if you could move away to a new lab straight away, it would be worse if you had no arrangements at all. I actually found it fairly common amongst my academic peers to take a short position with their PhD advisers, and all of them went on to have successful careers (some in academia and some in industry).
This practice might be more common in countries and programmes like mine in France where the workload is very high after submitting the thesis manuscript and while preparing the viva, and somewhat less common when the workload after the thesis submission is low, or the funding typically lasts only until the manuscript submission and not the viva (like the UK), but it is not unheard of in a European academic setting.
I took a 4-month position with my PhD adviser after my PhD, as the viva preparations were overwhelming and I did not have time to look for another position earlier (or sleep, really). The only "consequence" I saw when applying with that information on a CV is that the short position was considered an extension of my PhD work, and not as a standalone postdoctoral experience. But, as long as it is just a short position (up to 6 months I'd say), you can see it as a time to improve your CV and publication list while applying for your first "proper" postdoctoral position.
I never aspired to end up in Oxbridge or Ivy league, but I am currently being considered for faculty positions at some good and some excellent Universities (in my opinion). It all went quite according to plan for me. I do not feel that my success in my current faculty applications, or my academic career, was in any way affected, negatively or positively, but a 4-month postdoc with my PhD adviser.
One more exception on when it is okay to accept a position in the same lab after the PhD (which does not apply to your case but I am mentioning it for completeness) that I have seen (in the UK) is obtaining postdoc funding (for oneself) through a Fellowship, to which one can apply while finishing their PhD. Since obtaining a Fellowship means you are self-funded (and the funds were awarded to you by name), having successfully secured research funding will become the strongest line on your CV and the institution where you chose to do it will become less important.