If she signs a contract, pays in full by the deadline and finalizes the design by the deadline there isn't an issue. Calling six weeks out isn't a flag unless combined with other (troublesome) behaviors.
Sometimes "little things" pop up rather unexpectedly so people want to get married quickly. KWIM?
Some don't plan months in advance for every little thing.
It wouldn't automatically raise red flags with me.
It could be:
-shotgun wedding (they do still happen these days), or other rush-job (seriously ill grandparent etc)
-previously booked caker let her down or she decided they don't want her anymore
-Aunt Sue was going to make it for them but she has just realised she is a novice and begged them to get a "real" cake
-venue/caterer change and cake is no longer included in her package
-for budgetary reasons perhaps they can no longer afford their previously booked caker
-likewise, for budgetary reasons perhaps they were planning on a Costco cake and have just found some budget for a "real" cake
-perhaps cake just wasn't a priority for them
-perhaps they had planned on ordering a cake ages ago but something kept cropping up - first it was Christmas, then busy at work, then they took a vacation so were concentrating on that, then Easter came along, and all of a sudden her wedding is right on top of her and she's just realised she hasn't got a cake sorted (!!panic!!)
There's a few reasons I have seen/heard myself in last-minute cake orders, and none of them ring alarm bells with me.
Just ask her, her answer will tell you all you need to know 
I once did a wedding TWO weeks in advance. I just happened to be available, and what they wanted was simple. They had been engaged for ONE week before they called me He was in the army shipping out. It was kind of romantic But ya, make sure they pay up!
Don't worry about it... I just booked one 12 days before the wedding for 120 people. I also just booked 2 for the first half of July... as long as the pay and sign the contract, don't worry about it.
As said in previous post it could be a number of things. As long as everything is finalized when payment is received and she understands it's final, you should be alright.
Just last month, I had a bride book me on Monday for her wedding on Saturday! Of course, the cake was fairly simple for obvious reasons Her original cake decorator backed out for some reason. I just told her I needed the contract signed and paid in full the same day she called. She came with cash and was just super relieved to have someone who would make her a wedding cake!
As long as she's willing to sign and pay, I wouldn't worry about it!
My cousin got married a few years ago to someone he met while working in Korea. They came back here to marry and she had no idea she would have issues booking a wedding cake the same week they got married...they ended up with sheet cakes from costco or something..... Some people don't realize wedding cakes should be booked quite a bit in advance... The last wedding I went to they didn't even have a cake - just a buffet of desserts and squares... just wasn't important to the bride- no one seemed to miss it either
I had a bride book 6 weeks out. She had planned on making a 200 cupcakes herself but then as the date got closer she realized that she just didn't want to deal with it. She paid everything in full when we met and she's been really great to work with.
I did a wedding cake with less than a week's notice.
The bride hadn't planned on having a cake at all, but then changed her mind.
I got her to pay in full, directly into my bank account (which is a secure way of doing it here in the UK - I think banking systems are different in the UK and US).
No problems at all.
Ditto to all these, we get last minute wedding orders all the time, and they are almost always great to work with and get you the money right away because they are just so grateful you are able to do their cake!
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