Propagate from a Root-stock

[GF3]

I have a Plum tree (Blue Tit) growing on a Pixy Root-stock. I got the tree, bare-root, last November (2019). Today I noticed a small shoot coming off the root-stock - could I propagate this, and grow another tree from it? If so, any idea what it would likely produce? What is used for grafting plum trees onto?
Many Thanks.

[ameno]

Plum rootstocks are of varying species. Pixy is originally a seedling of St Julian A (the most common plum rootstock), which itself is Prunus insititia (same species as damsons and mirabelles).
If you took a cutting and gre it, it may produce fruit, but there's no guarantee the fruit will be nice, nor even that the tree would be small, as it's not just the rootstock itself which determines size but also the graft between it and the scion.

If you want a project, a better idea would be to take a cutting from the rootstock, grow it until it is at least 1cm thick, then use it as a rootstock for another plum tree. Cut a length of stem one winter from a friend or neighbour's plum tree you like the look of, the graft it on yourself.
Bear in mind, though, fruit trees need to be propagated from hardwood cuttings. This means you would need to leave that shoot growing from the roots until winter before removing it and using it as a cutting. This will likely result in the top of the tree growing more weakly this year (although as long as you limit it to one suckering shoot, it shouldn't do any permanent harm).

[mrbadexample]

Some info here.

[GF3]

Thanks for your replies.
I was thinking of using the "Air Layering" method to propagate (the shoot is branching out from the root-stock stem, below the graft point) - what time of year would be best for this method? I'm not really bothered about how big the tree got or what it eventually produced. I just thought it would be an interesting thing to do, rather than just cut the shoot off.

[nickdub]

Thanks for your replies.
I was thinking of using the "Air Layering" method to propagate (the shoot is branching out from the root-stock stem, below the graft point) - what time of year would be best for this method? I'm not really bothered about how big the tree got or what it eventually produced. I just thought it would be an interesting thing to do, rather than just cut the shoot off.

As long as the off-shoot is fairly whippy and long I wouldn't bother air-layering - just bend it down until it touches the soil then put a brick or stone on it at that point - after a year you should find that it has rooted where it touched the earth and you can cut it off from the main tree and then have a new rootstock to graft on to.