if else statements to calculate rates when data is in long form

A sample of my data is available here.

I am trying to calculate the growth rate (change in weight (wt) over time) for each squirrel.

When I have my data in wide format:

squirrel    fieldBirthDate  date1       date2       date3   date4   date5   date6   age1    age2    age3    age4    age5    age6    wt1     wt2     wt3 wt4 wt5 wt6 litterid
22922         2017-05-13    2017-05-14  2017-06-07  NA      NA      NA      NA      1       25      NA      NA      NA      NA      12      52.9    NA  NA  NA  NA  7684
22976         2017-05-13    2017-05-16  2017-06-07  NA      NA      NA      NA      3       25      NA      NA      NA      NA      15.5    50.9    NA  NA  NA  NA  7692
22926         2017-05-13    2017-05-16  2017-06-07  NA      NA      NA      NA      0       25      NA      NA      NA      NA      10.1    48      NA  NA  NA  NA  7719

I am able to calculate growth rate with the following code:

library(dplyr)

#growth rate between weight 1 and weight 3, divided by age when weight 3 is recorded
growth <- growth %>%
    mutate (g.rate=((wt3-wt1)/age3))

#growth rate between weight 1 and weight 2, divided by age when weight 2 is recorded
merge.growth <- merge.growth %>%
    mutate (g.rate=((wt2-wt1)/age2))

However, when the data is in long format:

squirrel    litterid    date    age wt
22922       7684    2017-05-13  0   NA
22922       7684    2017-05-14  1   12
22922       7684    2017-06-07  25  52.9
22976       7692    2017-05-13  1   NA
22976       7692    2017-05-16  3   15.5
22976       7692    2017-06-07  25  50.9
22926       7719    2017-05-14  0   10.1
22926       7719    2017-06-08  25  48

I cannot use the mutate function I used above. I am hoping to create a new column that includes growth rate as follows:

squirrel    litterid    date    age wt      g.rate
22922       7684    2017-05-13  0   NA      NA
22922       7684    2017-05-14  1   12      NA
22922       7684    2017-06-07  25  52.9    1.704
22976       7692    2017-05-13  1   NA      NA
22976       7692    2017-05-16  3   15.5    NA
22976       7692    2017-06-07  25  50.9    1.609
22926       7719    2017-05-14  0   10.1    NA
22926       7719    2017-06-08  25  48      1.516

I have been calculating the growth rates in excel, however I would like to do the calculations in R instead since I have a large number of squirrels to work with. I suspect if else loops might be the way to go here, but I am not well versed in that sort of coding. Any suggestions or ideas are welcome!