DH and I went out for a meal when my parents came down to meet DC1 when she was only a couple of weeks old (ebf but I left expressed milk). We were out about an hour and a half.
I enjoyed it but regretted it the moment I walked in the door when she was screaming and red and clearly had been in full blown screaming mode for some time, not just a bit grumpy/ fussy or anything... and my mother casually said they'd obviously had to leave her in the bouncy chair "making a bit of fuss" so they could eat their take away - for some reason I assumed that they, like me, would not leave her to cry and would hold her and take it in turns to eat or eat one handed if she cried when put down, like I did... since then my mother has outright denied they left her to cry, but she casually admitted it at the time when it hadn't crossed her mind anyone would do anything other than ignore a 14 day old screaming in a bouncy chair so they could eat a take away at a leisurely pace, even though they were only babysitting for a couple of hours max
After that I didn't leave DC1 til she was 6 months old (with DH), DC2 til 4 months old (no choice as I was admitted to hospital with bronchitis, wouldn't have otherwise) and DC3 at 5 months old with DH as I went back to working evenings, but only ever with DH. My kids started staying over with DH's parents at around 1, but we don't live near my parents and they've never babysat since that first time!
I haven't been out for drinking and clubbing since before having kids, but that's because I lost interest in doing that long before I even got pregnant the first time, it just doesn't hold any appeal any more. I went to a few hen nights but left early - its lost whatever dubious charm it once had.
I think you'd be fine leaving a 6 week old with DH as you're on the same page leaving to cry etc. wise, but you might get engorged or just be too knackered and not in the mood... I have no idea what you should do - you might regret cancelling and the evenings petering out and stopping happening, but equally you might still be very hormonal at 6 weeks and be exhausted, physically uncomfortable and not in the mood at all...