Cute. On this side of the pond my country (Sweden) hopes to have everyone vaccinated by maybe this autumn. It will probably take longer than that. Why? Because of a constant lowering estimate from the medicine companies how many doses they can deliver. The only ones who have started to receive vaccinations are people over 70-75+. 15% over 18 years of age have received one dose, 6% have been fully vaccinated.
It's a farce. It seems open trade is fine and dandy unless it's something actually important. Astra Zeneca is a British/ Swedish medical company, yet basically all doses seem to end up in British hands.
Being a Swedish company is less important than Sweden's domestic manufacturing capacity, which I believe is not very high (likely owing to very high labor rates in Sweden versus labor rates in other countries). Canada had considerable manufacturing capacity until as recently as the Harper Government too, but they elected to eliminate that manufacturing capacity in favor of dependence on the US and UK.
Nations just aren't exporting vaccines in large quantities until their domestic polities are taken care of, not if they are democracies. The people won't allow it, and there are very few exceptions to that maxim. It's easier for governments in Russia and China to do it to try and score points, because they aren't beholden to their domestic supporters. Fair ain't got nothing to do with it. It's politics.
Once the US has largely vaccinated those who want it domestically, though, the floodgates are going to open, especially for the easily stored and administered single-dose J&J shot. Massive exports will start shortly thereafter. They have to get their own house in order first, though.
I expect there will be a much more diversified global vaccine manufacturing base after this experience. Diversification is good, and should help eliminate bottlenecks in future.