How to preserve squash
If it's a summer squash you could maybe try freezing it? Since it's being turned into baby food anyway, preserving crisp, freshness isn't high on the list of priorities?

Disclaimer: I have no experience freezing summer squashes, but a quick google came up with this and it seems to make sense: http://www.pickyourown.org/freezing_summer_squash.htm

A further search reminded me that Alton Brown covers freezing stuff in an episode of Good Eats. He explains why the above blanching method works for many vegetables.