Nanny is Moving. What's proper etiquette when finding new nanny?

Hi all! I just found out our nanny who has been with us for 6 months will be moving in two weeks. I'm sad to see her go, our son (14m) loves spending time with her and I feel so lucky we found her as quickly as we did. I'm a first time mom and she is the first nanny i've ever had, I was so nervous when starting the search and now i feel very nervous again especially since I am hoping to find a replacement in the next two weeks before she leaves.

I found her on nanny lane pretty quickly so i don't have much experience in proper eitquette when interviewing potential candidates. My main questions is about background checks. I love that nanny lane offers these, but I'm not sure when in the process I should request them, or if someone might find it "offensive" in a way if i initiate it? It sounds silly but I'm not sure if that's a common tool that's used when hiring or if it's just a resource available that most people skip over?

Any help or tips that may be useful in my search would be appreciated, questions to ask or topics of concern. My main priority (as I'm sure is everyone elses) is that my son is safe and engaged with whoevever we hire, I just want to make sure I'm going about it all the right way.