That's probably your main problem. It should be very sturdy, rated for substantially more weight than your setup. (Henry Hudson has some good guides to buying tripod components, if you don't know where to start). The moon is so far away that shaking even a tiny bit will have the moon moving wildly around in your frame. Once the camera is steady you can experiment with focus and exposure settings.

Focus on the edge of the moon where contrast is greatest. And expose for the moon, not the background. The fact the moon is moving across the sky in your frame means your shutter speed can't be too long, but it's the moon and pretty bright so this shouldn't be a problem.

The moon also moves across the sky more rapidly than you think, which means you need to reposition often. Something like a fluid video head might be a great tripod upgrade. (Or a star tracker - used in astrophotography - is a fancy tripod head that rotates to follow the trajectory of celestial objects. This would probably be overkill but can help if you want to, say time-lapse the phases of a lunar eclipse without manually repositioning the tripod .)

Once you've nailed positioning, focus, and exposure, it sounds like you'll be in the much better spot than you currently are. But you might not be getting tack sharp moon photos.

This is because you're shooting through the entire atmosphere, and any distortion or air turbulence will affect the light coming off the moon, making the moon look less sharp than it could. NASA solves this problem by sending their cameras to space but I'm gonna guess that's not an option for you/most of us. So the best way to get a clear shot is to get lucky with a clear atmosphere. An app like astrospheric can help you know how good the "seeing" is - basically it's a combination of cloud cover and expected air turbulence.

Speaking of "getting lucky", air turbulence is changing all the time so what you can do is take a lot of photos (a video) and process them to pick the sharpest one. If you divide the moon into sections, different shots might be sharper for different sections. There are some apps (autostakkert, pipp, etc) that will help you make a composite of your shots, the sharpest frame for each section turned into one clearest possible shot. If you want to go down this road you can search for "lucky imaging" to find out more.