early ultrasound question

Hello lovely ladies I am 4 weeks and 6 days and I am wishing I could hear babies heart beat already ❤️ my insurance/doctor won't do an ultrasound until 12 weeks unfortunately. Has anyone gone to a private woman's clinic and gotten an early ultrasound at around 8 weeks just for peace of mind ! Or is that silly? I know I am going to be worried my entire pregnancy because that's just me but I'm really trying to be less stressed for babies sake and mine ! Any advice helps 👍🏼