Duplicated IDs pandas

Question

I have the following dataframes (df1,df2):

ID	Q1
111	2
111	3
112	1

ID	Q2
111	1
111	5
112	7

Since the IDs are duplicated, I want to reinitialize them, using the following code:

df1.sort_values('ID',inplace=True)
df1['ID_new'] = range(len(df1))
df2.sort_values('ID',inplace=True)
df2['ID_new'] = range(len(df2))

in order to have smth like this:

ID_new	ID	Q1
0	111	2
1	111	3
2	112	1

ID_new	ID	Q2
0	111	1
1	111	5
2	112	7

The question is: are we sure that the ID_new will be the same for df1 and df2? For example: is it possible that ID_new = 1 corresponds to the first ID=111 in df1 and to the second ID = 111 in df2?

If yes, there is another way to reinitialize it in a more robust way?