Prior to the 14th and 15th amendments, the US Federal Constitution and the Federal laws passed under it neither allowed nor denied anyone the right to vote. The decisions on who would and would not be allowed to vote, including for members of Congress and for President, was wholly in the hands of the sates, and were regulated by the various state constitutions and laws. A few states permitted women to vote, and at least one permitted free blacks to vote, at least for a period of its history. The Federal government had nothing to say on the matter.
In at lesat one case the US Supreme Court refused to consider such a question. That was the case of Luther v. Borden, 48 U.S. (7 How.) 1 (1849) which grew out of the Dorr Rebellion
The state of Rhode Island, had retained its pre-revolutionary charter (dating from 1663) as its constitution, and required the ownership of a significant amount of landed property as a qualification to vote. The Wikipedia article on the rebellion (linked above) states:
By 1829, 60% of the state's free white men were ineligible to vote (women and most non-white men were prohibited from voting).
In 1841 a group led by Thomas Wilson Dorr held a convention to draft a new state Constitution, (known as the "People's Constitution"), and held ratifying votes on the draft. They declared that it had been approved by a majority of those qualified under the old laws as well as a majority of those voting and qualified under the new rules, and that it was therefore the valid constitution of the state. The old (charter) government said this was invalid and illegal. Attempts to establish the new government by force failed. However, a revised state constitution that greatly expanded voting rights was passed and took effect in 1843.
Luther v. Borden was a case of trespass against members of the militia acting under the charter government, brought by a supporter of Dorr. The plaintiffs brought extensive evidence (over 150 pages) intended to establish that the Dorr or "People's" constitution had been validly ratified by a majority of voters, and that the old constitution had improperly restricted voting rights. The case went to the US Supreme Court, where Chief Justice Taney wrote in the majority opinion:
The plaintiff contends that the charter government was displaced, and ceased to have any lawful power, after the organization, in May, 1842, of the government which he supported, and although that government never was able to exercise any authority in the State nor to command obedience to its laws or to its officers, yet he insists that it was the lawful and established government upon the ground that it was ratified by a large majority of the male people of the State of the age of twenty-one and upwards, and also by a majority of those who were entitled to vote for general officers under the then existing laws of the State.
...
The point, then, raised here has been already decided by the courts of Rhode Island. The question relates altogether to the constitution and laws of that State, and the well settled rule in this court is that the courts of the United States adopt and follow the decisions of the State courts in questions which concern merely the constitution and laws of the State.
Besides, if the Circuit Court had entered upon this inquiry, by what rule could it have determined the qualification of voters upon the adoption or rejection of the proposed constitution unless there was some previous law of the State to guide it? It is the province of a court to expound the law, not to make it. And certainly it is no part of the judicial functions of any court of the United States to prescribe the qualification of voters in a State, giving the right to those to whom it is denied by the written and established constitution and laws of the State, or taking it away from those to whom it is given; nor has it the right to determine what political privileges the citizens of a State are entitled to, unless there is an established constitution or law to govern its decision. {emphasis added}
Thus, until the passage and ratification of the 14th and 15th amendments, which forbid states to deny the vote based on race, national origin, and a few other grounds, the Federal Constitution had nothing to say on the point. States were required to grant the right to vote to women by the 19th amendment in 1920, and the 26th (1971) prohibited denial on the ground of age to anyone 18 or older. The 24th (1964) prohibited denial for failure to pay a poll tax or any other tax. The 14th amendment has been held to guarantee the equal weight of votes, in what was at first known as the "one man, one vote" rule (later "one person, one vote") and has been used to overturn individual and group denials of voting rights. But there were no federal voting rights in the years before 1865.
I am not aware of any writings by any of the "founding fathers" (say the members of the Constitutional Convention) that seriously discuss the possibility of a female President. But they did consider and endorse the possibility of a person being elected president who might not be qualified to vote in some of the states. They declined to impose, or permit Congress to impose, a property, or other variable, qualification on the president, even though many of the original states had property qualifications for voters. Options for this were proposed and voted down in the Convention's drafting process.
