Amongst all the flippant suggestions, including mine, there are a couple of serious ones.
So let's weigh up the points.
One reason for changing may be that you're having problems with the current instrument - too hard to blow, doesn't sound good, too small, lots of reasons in this category, but it doesn't seem to be the case here.
Although saxes have the same keys, same note range and music for each pitch, they're not the same. It's not only physical size, it's blowing and embouchure. Plus when you go from an Eb sax like your alto, to a Bb sax like the tenor, you'll hear different notes coming out, even though they're the same on the score.
When you first learn, you're developing basic skills, linking notes on the score to finger combinations, embouchure and breath control, and ear. Changing sax or mouthpiece or even reed affect one or more of those basic skills.
Messing around with saxes or mouthpieces at this stage is asking for trouble and I'd not expect you to find a teacher that supports having a tenor and alto at this stage.
However.... If you're flexible and can keep yourself mentally clear about what's needed for each sax it may work. What's usually ignored/dismissed in a discussion like this is that you learn to be flexible. You're not going to get locked into a single mouthpiece/reed combination. You're not going to become so dependant on a single reed that when it fails, you spend months trying to find one that plays the same. You'll find you're able to adjust quickly to new kit and evaluate it for what it can do, not whether you can adapt to it. And you won't be locked in to Eb or Bb.
The longer you leave trying other saxes, the more difficult it becomes, as you tend to lock in. If you've decided that Tenor's have a sound that appeals more, maybe take Jeanette's advice. Also listen to what Jazzaferri says. And if jbtsax joins in, as a teacher I expect he'll say something like "far too early"
I don't know if you drive or learnt to fly, but if the instructor pitched in a different car, or you had a mix of instructor plus parent/friend with licence helping, you'll remember the difficulty of adapting to different clutch/brakes/steering/size/gear change points on each car...
There's no-one but you can make the decision. But weigh the consequences with the benefits. And your heart.