Absolutely, but first she would need to defeat the GOPe and she needs to make a firm commitment, not any version of a long drawn out “considering it” tour.
Absolutely, but first she needs to get her kids on board. I suspect Track and Willow weren't the last time. Track would receive flack for his brief marriage. Willow is through school so probably is in a stronger position this time. Bristol has shown she can take it and I have plenty of faith in Piper. Trig probably won't personally notice his own flack, but he will notice a change in his life style, which he may or may not tolerate well. And the family will certainly notice Trig related flack and has to be willing to take it. Any perceived negatives to him will be shouted against the parents. She has done plenty of traveling during his life, so hopefully he'd be ready for it. If her family is really on board she can take the worst the left and the GOP-e can throw at her.
If she wants to run and can line up her family for it then I agree she should come in early. Not necessarily earliest ever - historically someone had probably already started by this time - but early enough to minimize the field of conservative wannabees. Come in early enough and big enough to produce a series of voices on the right saying "I was thinking about running, but am endorsing her instead." Let the GOP-e have the divided field instead. And if the Democrats try to run Hillary make her look old and tired out by comparison.