The Constitution has no guarantee to a right of privacy.
But the Supreme Court said it does and lower courts, such as the one she was being confirmed to have to go by what the Supreme Court says. Once on the Supreme Court she can read the Constitution anyway she chooses.
Yes, the Constitution does include a right to privacy. A right to privacy was understood to exist at the time the Constitution was written, and the ninth amendment makes clear that the enumeration of certain rights in the bill of rights does not mean that other rights are not still reserved by the people. The right to privacy has been, from the beginning, the key to understanding various of the amendments and clauses of the constitution, such as the defense against search and siezure.
But the definition of privacy has always been those issues at which there is no public interest. There is plainly a public interest in protecting the lives of all persons. The problem with Roe v Wade is that it used an absurd legalism to infer that since the fourteenth amendment did not define unborn people as persons, they did not even have the right to life, and thus found that there was no legitimate state interest in the regulation of abortion.
As long as you ignore the Fourth, Fifth and probably the Third amendments it doesn't. And the Ninth as well.