Yes, the Batteries would have gone over together, and unless detached to another unit, would have engaged in the samecombat operations . Stanton's "WW II ORDER of BATTLE" gives a little fill information, as follows:
125th AAA Gun Battalion (Mobile) arose from from Separate CA BN AA-gun, at Camp Haan, CA, 24 May 43; it was redesignated from CA to AAA, 28 June 43; it departed Boston P/E, 1 Jul 44; arrived England 8 Jul 44; arrived France-ETO, 24 Sep 44. arrived NY P/E, 25 Mar 46; inactivated at Camp Kilmer, NJ, 27 Mar 46.
Rhineland, 15 Sep 44 / 11 May 45 Ground Combat , EAME Theater, thru 8 May 45 Ardennes-Alsace (Bulge), 16 Dec 44 / 24 Jan 45.
Location a war's end, 15 Aug 45: Stenay, France.
I note that the QUEEN MARY transported 14,533 troops,sailing from NY P/E, 1 Jul 44, arriving Gourock, Scotland, 7 July 44. Do you know if he was on QM?
I am sure that all of the above is redundant, since you probably have it in the unit's history you mention.
Go to GOOGLE, enter , which will bring up all of the Infantry Divisions.
Scan down each to ATTACHMENTS, look for AAA,andyou just may come across the 125th.
It is a little trouble, but could be well worth it.
Mind you, the unit could have had numerous such ATTACHMENTS, so you'll want to scan them all.