I have not had an ultrasound yet, and just found out my upcoming appointment does not include one (12w 4d)

I am 33, and this is my first. I found out at around 6 weeks as this was unplanned. It was hard to get an appointment to get the ball rolling in general.

When my upcoming appointment was scheduled for this Thursday, I was under the impression that an ultrasound would be involved. I had stressed at my previous appointment that I will not be home for the remainder of July due to a preplanned non-refundable vacation (that my partner and I are now treating as a babymoon). As it turns out they only have me down as listening to the heartbeat with a doppler, and some bloodwork.

Does this sound normal? To not have an ultrasound at almost 13 weeks? I won't be back until I'm 16 weeks and change... is this bad? Should I try to schedule something at one of those independent "spa" places (knowing it's not a medical scan) just to see the baby?

Please be kind, this pregnancy was unplanned and I feel like I'm scrambling to figure out what I'm doing, how everything works, what is normal and when to worry. Thanks all, wish me luck <3