All firearms and ammunition are already federally taxed. Not just that, they are taxed in excess of normal goods specifically because they are firearms and ammunition.
https://www.govinfo.gov/content/pkg/...II-sec4181.pdf
§ 4181. Imposition of tax
There is hereby imposed upon the sale by the manufacturer, producer, or importer of the following articles a tax equivalent to the specified percent of the price for which so sold:
Articles taxable at 10 percent—Pistols.
Revolvers.
Articles taxable at 11 percent—Firearms (other than pistols and revolvers).
Shells, and cartridges.
It's also worth noting that although Heller did not address registration in the ruling, it wasn't because there was no opportunity to do so. In fact, the matter at the root of Heller was that DC required that handguns must be registered but prohibited registration.
Heller found that they could not prohibit registration because that amounted to a ban of all handguns. In the process of making that ruling, SCOTUS implicitly accepted the premise that registration of all handguns was reasonable--although there was certainly no explicit statement to that effect.