Someone posted an interesting link on a different thread (I'll see if I can find it) to a research paper that gave a case study showing how popular representations of scientific research are generally mobilised to reinforce pre-existing social ideas. I think attachment is sadly very much a case in point. While the research itself is moderate, quite nuanced, and most pertinent to the treatment of children in institutional settings, it has been co-opted as a kind of pseudo-scientific authority with which to reinforce pre-existing ideas about how mothers should behave around their children. Numerous posts on this thread corroborate this.
There are several misunderstandings that keep cropping up. One important one (that turns up on threads discussing 'attachment parenting' as well) is the idea that insecure attachment styles are profoundly dysfunctional, rather than generally well within the normal range of social functioning - some 40-50%% of people exhibit an insecure attachment style when tested as adults. A second misunderstanding is the notion that brief childhood experiences are immutably deterministic - for example that a single short experience such as a three-month separation will irreversibly 'damage' the child for life. Combined with the first misconception, you can see how the catastrophising begins.
The reality is that the only profoundly dysfunctional attachment style is caused by frightened or frightening caregiving, such as violence, parental psychosis or drug abuse, or severe neglect. This does have lifelong consequences and is difficult to remedy. But the vslast majority of parenting is perfectly adequate from an attachment perspective and it is deeply unhelpful to new parents, who are generally just doing their best, to suggest otherwise.
Yet another misapprehension is around how much parents can actually do to affect their child's attachment style. In fact the strongest predictor of secure attachment is the primary caregiver testing as secure in the Adult Attachment Interview. There is no evidence whatsoever (if anyone knows of any please correct me, I am always on the lookout) that a parent testing as avoidant or preoccupied in the Adult Attachcment Interview can affect the chances of their child's developing a secure attachment style through any methods such as bed-sharing or carrying a baby in a sling. That is to say, AP methods and constant maternal proximity to one's children may be appealing for any number of reasons but there is no evidence that they do anything to affect a child's attachment style.
Again the reality is that a style of interacting - and resulting attachment style - is transmitted by a caregiver through a billion tiny interactions every day, and not by single major events such as a 3-month separation or by techniques, length of breastfeeding etc. My own view is that, given that a secure attachment style can be learned via psychotherapy, anyone genuinely concerned that their own patterns may impede their children's developing a secure attachment style would be better spending their money on a good adult psychotherapist than on babywearing equipment or an extra large bed.
With the in mind, should the OP decide to pursue the internship as described, the thing to watch out for would be alterations to the relationship on her return. She would need to prepare for a period of readjustment as she resumed her relationship with the baby, and to have support for any difficult feelings that could arise if, for example, the baby took a while to respond to her again as she had done before leaving. If any long-term harm were to be done it would NOT be caused by the separation as such but through this rapprochement being badly handled, with a resulting knock-on effect on the subsequent relationship. If steps were taken to support the OP to avoid this outcome I do not see why she should not travel as described.
Again, it is really important that attachment not be seen as a cut and dried injunction to mothers to behave in a certain way. It is about styles of human interaction, it is more plastic than deterministic and there is plenty of scope for alternative caregiving arrangements with no loss of psychological wellbeing in the child. The key is to ensure happy ongoing relationships within the family and I see nothing to suggest that the OP would not do this.