Among the authors who wrote that Caesar really loved his daughter, is Christian Meier. I think that they refer to a letter of Quintus Cicero to his brother. Here is the only mention I've found of such a letter :

Caesar, for example, evinced proper self-control when his only child, Julia, died in 54. Quintus reported on Caesar’s deportment to his brother, who replies “About the virtus and gravitas which Caesar showed in his terrible grief, I derived great pleasure from your letter.” (Q. fr. 26/3.6(8)3) in Presidential Address 1997, Chicago, Illinois, Home and Forum: Cicero between “Public” and “Private” by Susan Treggiari (Stanford University).

In his correspondance, Cicero made a few allusions to Caesar's grief :

To Quintus :

I have a letter of Caesar's dated the 1st of September, which reached me on the 27th, satisfactory enough as far as the British expedition is concerned, in which, to prevent my wondering at not getting one from you, he tells me that you were not with him when he reached the coast. To that letter I made no reply, not even a formal congratulation, on account of his mourning. CXLVII (Q FR III, 1)

To C. Trebatius Testa (IN GAUL) :

As you were not with my brother Quintus I did not know where to send a letter, or to whom to give it. I am anxious to know how you are and where you mean to winter. For my part, my opinion is that you should do so with Caesar; but I have not ventured to write to him owing to his mourning. CXLIV (F VII, 9)