I make timber paddles and trust me that is tough enough.

I think that to make a carbon one that is similar in weight and strength to the current ones available to buy, without the autoclave and tooling would be quite difficult.

Anton is right, you won'ty get same weight/stiffness. But if you don't mind a bit heavier, and wanna play around, it is not hard at all for a one off

Just time consuming as for a one off you'd probably not mould it.

Divinycell core, shape, coupel of layers of about 200gm satinweave and a 3oz twill or satinweave glass over the top as a sacrificial / durable layer. . Gelcoat and sand back, polish.

If you can score the d'cell for free as offcuts, that is about a $50 - 60 materials kinda job.

Alternate:

Delrin foam - it is sorta halfway between polystyrene and d'cell, in about 6mm sheets for use under laminated wood flooring. Really damn cheap.
Shape, then insert 6mm ish carbon tube up the middle in a couple of places (it is like $5 a metre)
Laminate up with maybe 3 x 3oz glass and it will be damn stiff.
$20.

Another alternate - balsa with 2 x 3oz satin / twill weave glass. Probably stiff enough. If not, again some carbon tube up the guts.