No, for two reasons:
First, you seem good at managing SDRs. This is a skill. Managing entry-level sales professionals can try the patience of the best of us. So you seem to have a super-power here.
Second, hiring an AE to take over the SDRs is unlikely to work as well as it does today. Most AEs do not know how to manage other sales professionals. And most AEs are closers and don’t know how to manage the goals for SDRs properly, either. They tend to treat them like their sales administrative assistants.
So if you can, I say push on. Hire an AE or two, and another SDR. Get them all working. Then bring on a true VP of Sales.
But if you can’t handle it, having the SDRs report to the AE is better than nothing.
You can also hire a head of marketing and have the SDRs report to her or him. Many demand gen leaders these days have managed a small SDR team.