Will female guppies be better off without male guppies?

You should move your guppies to the new tank as soon as you get it. Since your current tank is undersized and uncycled, rather than spend weeks to cycle the new tank and risk the guppies dying in the undersized uncycled old tank during the same time, they have a better chance to survive in a bigger tank even it is uncycled too. More water means lower concentration of ammonia and nitrite.

A little note for you when you transfer them. It is the best to transfer as much water as possible before move the fish over. Since fish dislike sudden change in the water perimeter, having some old water will help them adapt to the new tank and avoid temperature/PH/hardness shock.

What filter do you plan to use for your new tank? You have only mentioned a heater is on the way. A filter is more important.

By the way, since you are doing partial water change every day, you need to be careful about the new water temperature. It is recommended to have the new water sit in the same room for it to have the same temperature before using it for water change.